Yeah maybe there are are 2000 mountains, but how many have mountain bike trails? If there are trails then there is probably some organization maintaining them like the state or national park service who can also run the shuttles. Shuttles are also pretty cheap and can stop at multiple trail heads based off requests. You can also rotate where the shuttles go each day / week so if there's a more obscure trail/mountain then you can just wait until it comes up in the schedule. The towns would also probably want to run the shuttles as well since it will bring business to the area.

Ok, let's assume we want less people on the mountain, what gives you the right to go to the mountain then? Because you can afford a car? That doesn't seem fair. Also most people have a car so it's not restricting that many people. If we say only 30 people should go to the mountain a day that's way easier to enforce if we say only 2 shuttles of 15 are allowed. It's also fairer as who gets to go is just determined by whoever signs up first, as opposed to whether someone owns something.

I think many people would like to socialize. There's a loneliness epidemic and many people are looking for friends but don't know where to meet them. If I was looking for friends with common interests like mountain biking the shuttle up would be a great place to meet them. Just because I want to get away from civilization doesn't mean I want to get away from socializing, I hike regularly with groups of people and they mostly enhance the experience. If you aren't into that that's fine too, just put on your headphones ignore everyone and set off on the trail solo, nothing stopping you from doing that.

For the last point like I said usage can be controlled, even better then cars, but assuming the same usage a shuttle is less pollution then multiple cars. If like you said there are 5-6 cars at a particular trail head then one shuttle carrying all those people will cause less air and noise pollution and make it safer for animals.