There probably are ways to keep a catbirds.com running but as the difficulty increases the likelihood of the site's maintainers keeping with it decreases significantly. If the site tanks all of its hoisted content goes with it. Ask all the people that had their content wiped from MP3.com how that feels.
So from a content creator's point of view, why hitch their wagon to catvids.com? It costs them money and isn't guaranteed to be around in a year. They're also far less likely to make any money no matter how much traffic aggregators send them. Sticking with YouTube is way less of a hassle and gives them a far better chance to make money if nothing else to break even to keep making content.
The aggregators don't own or host the content in the system I am thinking of, they just consume and redistribute their sources. So if catvids.com goes away the creator's source is still online. It's also probably syndicated to a bunch of other cat video sites simultaneously from that one source. Thinking through it more, it's pretty much an RSS feed but for videos. In fact I would probably just use the RSS protocol if I were ever to try and get something like this off the ground. Have an open source aggregator template so it's easy to start one, and then monetize it by starting the first video source hosting as a service company.
I don't think it could ever take off though, the "Next YouTube" will be another massive corporate, closed platform with deep pockets or venture capital.
TrainVids.com doesn't get many hits so for now they rely on the source' perfomance, but CatVids.com gets millions of hits and they long ago invested in a redistribution layer. Meanwhile ContentCreatorMatt pays $5/m on his source hosting with burst protection should a video go viral. Hosting can afford this because they have thousands of creators who never get a hit video. While CreatorTom only submits to large platforms with redistribution so he doesn't have to pay for traffic.
I wouldn't use P2P nor expect people to host the videos at home because that would never work for the reasons you outline. But think of live streaming and how that distribution works and that is just one possible method an aggregator could choose to increase performance of slow sources.
The idea is to break up the video platform monoculture and make the space competitive again, so that there will be some variance in performance to end users depending on the aggregator they visit isn't an issue.