Putting on my lawyer hat for a moment....
I think ski area risk management personnel around Tahoe, maybe beyond, have likely been spooked by the preseason incident at Alpine last year.
Bear in mind that you're complaining about a resort that has a lease from the USFS, because you (understandably) think that the public should have access to public land. The law isn't necessarily intuitive.
A lease gives the lessee most of the rights and responsibilities of ownership - and especially, the rights of possession and exclusion of others - during the lease period. The owner can't even enter the land without explicit permission. Just as you, not your landlord, are responsible for injuries to third parties in an apartment that you've rented, the ski area lessee, not the USFS, is responsible during their leasehold.
Business owners take out insurance to cover potential exposure that they can't otherwise control. Often, it's required by their lease terms. (I know it is for my company's lease.) But it's a delicate balance as far as what to insure, because you try to limit your exposure otherwise as well. That's where controlling access (tresspass) is useful. And for ski areas, I suspect that's also where waivers come in. When you buy a day or season pass, you agree to waive a lot of the ski area's potential liability. If you're hiking, you haven't signed one. If you think those waivers don't matter, I suggest that you review some of the cases on skilaw.com.
Put simply, I'm not sure that Kirkwood thinks it has any other choice. I'm not sure whether they're right about that, but I'm guessing that that's what their thought process is.
The sledding ban is odd, but I believe that there's a similar one at Alpine, so I wouldn't be surprised if it were required by the standard USFS lease. I remember that there was just legislation, last year IIRC, to permit ski area USFS lessees to allow any activities other than skiing on their leasehold. There was even a question about whether snowboarding was technically illegal.