MunchMaybe so, but saying that not having the degreaser would completely "neuter" the pyro is a somewhat irrational statement at best. The only reason it's seen as "necessary" is because it's really good at making what you already had to do as pyro easier, not because it's completely impossible to play without it. All I'm saying is that as good as the degreaser is, it's not really all that necessary when you look back and remember that this thing didn't always exist. Sure, maybe some weapons could make a degreaserless pyro's life a bit harder (nothing specific actually comes to mind though, liberty launcher maybe?) but I think I'd still be able to get along just fine without it if the degreaser had never came to be.
It's ROLE is pretty much held together by being able to use the degreaser. Crit-flares, crit-axes and the airblast all require fast reaction times in order to more effectively defend against (good) spies or a strong explosive flank. While bloodsire's video is somewhat proof of concept from your perspective; it is ultimately, a corner case. Much like the sandvich is the accepted secondary for a heavy in HL and the Ambassador is effectively the accepted spy primary, there's a difference between "viable" and optimal. Some players can make the stock revolver work for them, but they ARE nerfing their damage output.
Getting along just fine does not mean you're performing at the peak of your play.
When it comes down to it, not using the degreaser makes you more vulnerable to heavies, engies with the mini . . . pretty much every hitscan class. Sure, you can handle soldiers and demos basically the same, but every other class can beat you 1v1 easily (except maybe the big pick classes). It's essential because it obsoletes the stock in most situations.