In general, I agree with you that anyone who wishes to climb should be able to do so, but with the caveat that you should have a minimum level of experience, from which we can infer skill, and fitness, and that it is ethically acceptable*. If you lack these, you are endangering the lives of hundreds of others. The particular problem with the South/Nepalese approach to Mt. Everest is that there are virtually no regulations: according to the Oliver piece, an ~$11,000 climbing permit fee, and a doctor's note. There are no limits on the numbers of climbers. Defining what a "true mountain experience" is is subjective and a massive grey area, but Oliver's piece highlighted how Everest from the South certainly isn't.
To your point about the sherpas freely choosing their form of employment, the sherpas are all but forced by economics into their jobs. (Oliver noted that not all sherpas are Sherpas, the latter being an ethnic group, the former being a job.) Those living in that region of Nepal essentially have to choose between poverty and being a sherpa. It's akin to being an Appalachian coal miner or Newfoundland fisherman. Do/did you really have much of a choice? These people need these jobs to survive, but they are all inherently dangerous. They still deserve regulations to afford whatever safety is possible, and the they deserve to be afforded respect. It is also a fair question to ask, is it morally justifiable to pursue bagging a peak at the expense of these people's lives, even if they are desperate for work. (Similarly we can ask is it morally justifiable to watch football or is the 2022 FIFA World Cup in Qatar? Oliver, a huge football fan, has previously addressed the Qatar World Cup.)
*It is my understanding that there are some geological features, particularly in the southwestern U.S. and Australia that are considered unethical to climb because they are sacred sites to native populations. There is at least one bona fide 4,000 footer, based on the AMC's 200-foot col standard, and officially surveyed, that is not recognized by any of the major hiking clubs because of ethics.