Here is a lot more detail on declaration boundaries and the players in land preservation in the area that impact why Kearsage North access is such an issue. Unfortunately to understand, there is lot of background.
The declaration boundary is the legal boundary of the White Mountain National Forest established by Congress. Unlike the western national forests that were predominantly established on federal land, almost all the WMNF was on private lands that were a mix of mostly private land located in established towns and in some areas unincorporated locations. Many towns were dependent on having land to grow on and wanted assurances that the WMNF would not continue to grow and swallow them up. Therefore, if you look at the WMNF map, the boundaries are definitely not straight in many locations. Some of it follows watersheds while in most cases rail corridors and highway corridors were excluded. In some cases, major landholders, like the Brown Company in the north country with political influence and the state of NH had influence over the boundaries. Other factors are that WMNF was funded under legislation to benefit flood control predominantly on the Connecticut River watershed as the towns along the river in southern New England got hammered by spring floods of epic proportions due to the stripping of the watershed of trees by wholesale logging. The Weeks act proposed to reduce this flooding by restoring the watersheds that feed major rivers and the intent was that the land would be purchased on a willing buyer/willing seller basis. The prior large landholders used a lot of heavy tactics to drive out the small landholders prior to the WMNF. Much of the land was clearcut and on occasion burned out hillsides and valleys clogged with silt and logging debris from logging operations who had no interest in hanging around for forest regeneration. There are large and small landholdings in the national forest, these are still private and state lands inside the declaration boundary, if they come up for sale, the FS can fund the purchase from their budget or from special appropriations and "ear marks" or accept donations of land. BTW, the forest service like any government agency can as a final resort use eminent domain but that is regarded as the absolute "nuclear option" with nationwide repercussions if it were ever exercised. Even going to court for such a clear cut case of the former Mt Cabot trailhead access in Lancaster was reportedly deemed to be too much a of risk.
Desirable or available land outside the boundary is a different story, the FS cannot buy the land unless the declaration boundary is expanded by congressional action and typically takes years and can get wrapped up in national politics. The last expansion I can remember off hand was Lake Tarleton in the SW corner of the national forest. It originally was done to protect a large portion of the lake from development making the remaining properties on the lake incredibly valuable. That decision has "come to roost" of late as the WMNF is proposing to do a major cutting program in the land they acquired on the undeveloped side of the lake. It will probably benefit the forest in the long run but in the short run it will be ugly and the folks opposed tend to think in the short term. The Green Mountain National Forest is in same predicament, the land was protected for sustainable multiple use yet there is pressure now to stop any multiple use other than total preservation. The WMNF when it does timber sales is required to set aside some amount of the proceeds for recreational improvements, in some cases, these funds ahve been used for parking but in general those special funds are syphoned off to pay for maintenance of existing lots. The recreational use parking sticker program built and improved many large parking lots on WMNF land over the years in the whites but that revenue seems to have dwindled as court cases forced the WMNF to restrict the fee areas.
During the Northern Forest era in the 1980s when large blocks of industrial forest land in VT NH and to some extent western Maine were coming on the market from Wall Street leveraged buyouts of the long term owners where the companies large land holdings were stripped from the local industries who were already dying for other reasons, substantial expansion of the WMNF was not politically sellable in Washington (Reagan Era and spotted owl era on the west coast). The backdoor was to create the Silvio National Fish and Wildlife Refuge and the Umbagog National Wildlife Refuge as a means to preserve lands in the north country outside the WMNF boundary. The Umbagog refuge is quite "small" confined to the Lake Umbagog watershed, while Silvio Conte's borders are far less defined and can stretch along the entire length of the Connecticut River watershed although each individual management unit is quite small relative to the WMNF. They tend to be an "under the radar way" of the federal government to buy land for preservation through a somewhat routine budget process and has bought some small amount of the Northern Forest Lands. The Pondicherry area west of RT 115 in Jefferson is an example of a Silvio Conte management unit. I have watched that area grow over the years, they are patient and tend not to pay high prices but they set the low end. When undeveloped properties come up for sale in that area, they usually are backstopped by a refuge offer, if the owner can sell if for more to another buyer, it gets sold. I expect the flurry of recent house lot sales along Rt 115 on what was once large forest tracts are probably disappointing to the refuge.
The final actors in the story are large and small independent non profits that have access to donor funds, the large national groups can be relatively agile when inholdings come up for sale and in some cases will buy blocks of land adjacent but outside the boundaries. Some buy to hold but some like The Conservation Fund (TCF) What We Do | The Conservation Fund
buy to redistribute to other organizations. Here is long history of the complex transactions leading to the Randolph Community Forest and the involvement of the Trust for Public Lands TPL) http://www.communitiescommittee.org/pdfs/randolphstory.pdf
If you go through the deed registries for many north country towns in the WMNF, TPL and TCF appear quite often. TCF have been very active near the whites especially in recent years since 2016 when they hired Sally Manikian formerly of AMC. She has been involved in several recent medium sized transactions along the Androscoggin usually adjacent to but outside the declaration boundary. Her "trademark projects" are some incredibly complicated transactions (similar to the TPL Randolph Project getting funding from multiple sources to protect land. Once the land is distributed, TCF and TPL goes on to other projects and local non profits own and manage them. Upper Saco Valley Land Trust is a smaller land trust that was referred to as having lands in the area along Kearsage road. The trusts may own the land outright or just own easements of various sorts that permanently limit what can be done on a block of "conserved land". Some of these easements allow public access and recreation, but no recreational improvements, some do not. It usually depends on the funding source and what the original owner's intent was. The problem is that easements have to be managed "forever" and many of the organizations entrusted with owning the easements are frequently underfunded local or regional non profit organizations usually run by very dedicated but underpaid individuals in charge managing a revoloving door of interns and employees on their way up. In theory there is money set aside when easements are accepted, but few donors are interested in donating to administer properties and pay the staff compared to contributing to buying a new easement. Therefore, many land trusts really want to have nothing to do with organized public access as that requires staff and expenditures "forever" unless there is dedicated endowment and requirement to fund it. This can be real problem in urban areas where conserved lands become the refuge of the unhoused. The state of NH sometimes becomes the party entrusted with conserved lands as the state does not require long term funding of the management of an easement like third party trusts do. The state in general has a poor reputation with maintaining the easements and in many cases like the Sunapee, Ossipee's and Nash Stream have been known to ignore their responsibilities under influence of political pressure. The state division responsible for lands is chronically underfunded and understaffed and generally the only way they will do improvements is on projects that will self fund. Parking lots rarely self fund unless located on a very popular spot like a lake so the state is probably not going to build a parking lot at Kearsage North. The WMNF could if they had the funding and interest, but they would need to buy land from a willing seller and given the demand for land adjoining conserved lands I do not see that happening on Kearsage Road unless someone passes away and leaves the land to the WMNF.
So it comes down to its desirable to most locals who have "paid their dues" by buying land in town to have conserved land near their property but they really do not want too many folks from away to access it, the WMNF has many other priorities and Kearsage North is a prime example or one that is too sticky to deal with.