That a company has the money and the scale to implement anything they choose to, trivially or not does not mean they will actually succeed in the marketplace.
Small companies doing one thing have something big companies do not: relentless focus.
What a startup can create that a large company cannot steal would loosely be defined as a social network; mind-share among people who believe that your company is the go-to place for your service.
If you have built your service on top of Facebook, it will be very difficult to build your site so that you, and not Facebook, are what your customers thinks of when they think of your product. If it's truly a killer Facebook app, they will likely even be happier with a slightly inferior but fully integrated solution. Because they control the social network, the mind-share, that fuels your app.
If Google's Sergey, Larry, or Schmidt were as ruthless as Zuckerberg, I have no doubt that Youtube would have been left to die.
I said that Google had the option of letting Youtube weaken, and buy them at a discount...or fully letting them die out and have Google Video dominate. Each decision with a different risk/reward ratio. They chose the lowest risk/reward since $1.6 billion is probably a relative drop in the bucket for them.
Things just aren't that simple.
Viacom is simply not interested in running a money losing venture, otherwise they would have bought Joost instead of partnering with them. Disney didn't need the Youtube brand when they already invested heavily in go.com back in 1998. Look what happened to Hotmail dominance after Microsoft bought it. And what is Apple's experience with web apps?
So yes, things just aren't that simple.
And I could have bought McAfee, I just lacked $7.7 billion.
Relentless focus on the above factors (content, mindshare, usability) helped them win - have I missed any?
By parking it under the google brand they may have made a mistake. Another - possibly small - effect of that is that you have two steps before getting to a site, video.google.com, is less convenient than youtube.com, and much less easy to promote as a brand separate from the search portion of the site. Many people read 'video.google.com' the same way they promoted 'images.google.com', as a search engine for online videos (which it now has become, for the most part) instead of an easy way to share your videos with your buddies and the rest of the world.
I don't think it will be possible to quantify this effect, but I notice that microsoft named their search engine 'bing.com' after several tries of doing it as a subsidiary, and that google has not attempted to bring youtube.com under the google domain as the replacement for video.google.com (which still exists), it is now the 'search' arm of google for video, returning youtube.com mixed with other video results, just like what you'd expect.
Further thought: google video was 'better' in that it had higher resolution videos, and it displayed more of them on the screen at once. While youtube had one low resolution video. It was quicker to load and to run, and more suited to slower machines (perhaps especially mobile phones, whence videos oftentimes came?) Google video has always annoyed me in this sense. I note that now, they've increased youtube video resolution (it's 'better'), and also snipe: upgrade to a "modern" browser. Although understandable, it isn't the path to max adoption, and max. network effects