The scale of the company prevents meaningful competition, that's the issue, not necessarily that they can't affordably review the 49 years worth of video.
That problem in particular isn't really one that competition would solve, because it's fundamentally a demand for censorship, and more competition would make censorship harder. Which is maybe a good thing anyway.
The biggest problem there is that all the hosts want you to use their search and do what they can to get in the way of any third party turning them into a dumb pipe. But this is where some kind of P2P service could really have an advantage, because it doesn't have to care about that -- let it be a dumb pipe on purpose and it wins, because there are a thousand companies who would love to be in the video search/discovery business and not have to pay the cost of hosting the videos or worry about a centralized third party host locking them out next week.
The problem was never the scale of the company. If YouTube was instead 100 different companies, there would still be a total of 49 years worth of video being uploaded every day which nobody would have the resources to review. Each company would have 1% of the video but also 1% of the revenue and the cost would be just as insurmountable.