The word subsidize carries a negative connotation. How about we use “support” instead.
In a state that markers itself on tourism, supporting operations like ski areas and summit facilities seems reasonable.
As far as Cannon summit vs. Washington, I think that’s an apples - oranges comparison. At Cannon the top of the tram is the summit building.
Both the Autoroad and Cog fully (ruthlessly?) exploit and monetize the value of the publicly owned mountain and its summit. They should pay well for that privilege.