I suspect lots of young people would happily volunteer if it meant their life could return to normal. Heck, I'd bet even for the current strain, with a ~0.1% risk of death for young people, quite a few people would volunteer to get it if it meant they could get out of lockdown.
I personally work from home (as one of the privileged few being a programmer) and when I do go outside I take social distancing serious. My health in general isn't great although I'm not old (early 30s) and which is why I don't leave my apartment much anymore. I live in a college area and young adults are still going over to each others apartments and without practicing social distancing when going out to buy groceries. I'm in Quebec for context. I've heard it isn't much different in the USA.
Maybe the (possible) solution could work without young people on board.
That's my point: the young adults don't want to comply with the social distancing, so if someone said "hey, if you let me infect you with this virus that has a 1/50,000 chance of killing you, you can no longer get/transmit the more dangerous strain so you don't have to social distance any more", a lot would take the offer.
That doesn't matter. The reason why everything is closed is hospital capacity. That impacts everybody. If you had a car accident you may not get all the help you need.
14% of people may need hospitalisation and you want to focus your efforts on that group. There is almost no young people there.