The only one that might work is if they charged a reasonable fee and only allowed people that had uploaded government issued IDs and accepted liability for their accounts. That might help sufficiently deter bad actors and reduce labor costs to sift through all the garbage.
That is completely ignoring the network effects of everyone being on YouTube. The profitability of an alternate website while YouTube still exists has nothing to do with the profitability of a YouTube without music.
Competition won't change it. All competitor's will behave the same under the law's incentive. It may be hard to believe, but most of the tech companies are pretty rational. If the copyright laws favor normal users more, and have stronger punishment for spurious copyright claims, then the tech companies will implement it.
It's like blaming American Football for being too violent. My opinion is that the rule of the game make rational players behave that way, if they want to win. Basketball and Soccer are less violent because the rules are different. I can imagine a world where systems like content ID and spurious copyright claims are much rarer, if we have better copyright laws that encourages a different set of behaviors.
The laws and policies driving YouTube's ContentID were built when the content owners had YouTube over an existential barrel: had YouTube not come to a solution, they could have sued it into oblivion. The resulting implementation massively over-corrects in that direction. Barring a legal change to de-fang the content owners (or to impose penalties for false copyright claims), nothing changes.