Because it is not a solution at all, you are just adding a cost to people who are creating content and a cost to people just looking for something to watch. This is not a streaming service where you are looking at licensed films or series or in house productions where a cost to the content is understandable.
What we have is a video hosting site that is mainly used by regular people to upload a myriad of random content, if you tell someone that just wants to upload videos of their cats for other people to see that they have to pay a monthly subscription for that they are just gonna skip it altogether. On the other hand if you tell another person that just wanted to see a video of some random cute cats on the internet that they have to pay a subscription to watch footage of some pets they are just gonna find them someplace else. This is all just the majority of people who use these sites, I'm not taking into account actual specific content creators yet, this is just your random every day people.
On the hand of actual content creators you are giving them additional costs on top of the costs they already have to produce their content, and taking into account how most of these sites work their content would be taken down for something very small that could be considered a breach of the terms of service. Given that this would be a paid service that is just a massive turn down for anyone trying to distribute their content, why would I even think of uploading to this place when I am paying them for the service and they take my stuff down? I'm not gonna get the money I spent on the hosting back and I won't be making money off the video, on top of the costs I already incurred by making said video.
Could the paid model work eventually? Maybe, but it is not something that independent content creators or regular people can or are willing to pay for as of the current state of most video sites. Youtube is far from perfect, and their monetization scheme is downright crooked, but making a new video site and telling everyone that they have pay to use it and still be beholden by similar terms of use like those in Youtube is just off putting, not to mention that they would still have ad revenue in some form because like it or not that stuff brings a lot of money for those platforms.
I think I should have been more clear in how this hypothetical site would operate. So, first of all, viewers don't have to pay. Only creators. Secondly, there might be a system possible that even though a creator stops paying the fee, the video can still be kept hosted, albeit at probably a sacrificed quality. Thirdly, since the site doesn't have to play by advertiser's rules just to keep videos up, the rules can be much more lax and much less schizophrenic. Fourthly, we don't need to replace YouTube. If people are willing to sacrifice a bunch to have their videos hosted for free, then YouTube is for them, but this site would be the premium version of YouTube that works directly for and with creators because they are the ones the site team would be beholden to now, not random advertisers and execs. Fifthly, you can still have advertising on the videos, which means even though creators are paying a monthly fee, with ad monetization, they may not even need to pay it and in fact, could earn even more money then on YouTube since the cut they receive is higher. There's also other possible ways content creators can pay for the service like giving machine resources over to mine cryptocurrency, should they choose to do so.
I do agree 100% that subscription services are getting out of hand, but we may be throwing the baby out with the bathwater here in our haste to deny the shitty ones of money. For some things, a sub is not only deserved, but needed. But if, for this particular service that actually needs a sub, if people can get past that, then I firmly believe a lot of good things can come from that. I truly think that someday, we will have to accept that if we don't want to get dicked around with constantly, then we need to start paying for hosting videos.