But I guess they could charge money to get to the head of the line?
But I will unapologetically and forthrightedly say that, yes, if we're going to assert that YouTube has certain responsibilities for the nature of the videos that it hosts, and that it turns out that the nature of those responsibilities is such that YouTube can't possible meet them, then, yes, YouTube as we know it should be essentially shut down, at least going forward.
I am NOT going to say we should deliberately craft the responsibilities in such a way that YouTube is deliberately shut down. However, if it turns out that they are incapable of applying even the bare minimum effort that we as a society deem it necessary for them to apply, then, yes, it is absolutely a consequence that YouTube as we know it today may have to be so radically altered as to be a different site entirely.
In the general case, when the law requires certain obligations of you as a business, and you as a business can not meet them, that does not mean that suddenly those obligations are not applied to you. It means that your business is not legally viable, and needs to change until it is. It may be the case that there is no solution to being legally viable and being profitable, in which case, your business will cease to exist. Just as there is, for instance, no solution to being a business built around selling torrent files containing unlicensed commercial content to people. You can't defend yourself by saying you can't afford to get the licenses; your suitable legal remedy was to never have started this business in the first place. There's some concerns around grandfathering here to deal with, certainly, but they can still be affected going forward.
There is no guarantee that there is a solution where a company exerting whatever minimal control they are obligated to assert by society is capable of growing to the size of YouTube. If that is the case, so be it. The solution is not to just let them go because they happened to grow fast first.
(My solution to freedom of expression is an explosion of video sites, where each of them has ways of holding the videos to the societally-mandated minimum standard, and no one site can do it all because they simply can't muster the resources to be The One Site, because as they grow larger they encounter anti-scaling effects. Given how increasingly censorious Silicon Valley is becoming, as we are now into censoring the discussions about censoring discussions like the recent removal of Project Veritas from Twitter for its discussion of Pinterest censoring pro-life films, I expect this to increase the range of expression, not diminish it.)