Think of it as a small computer - just as my computer has multiple apps capable of playing video of different sorts, there isn't a single "video system" on the phone, but different apps that can display video.
If you disabled the YouTube app and flash player (if the phone has flash - the most recent don't) I guess html5 video might still play in the browser, but you'd have removed some ways it could play. And if the built in browser doesn't let you control video playback to your satisfaction you can use a different one (one advantage of Android - there's almost always an alternative app). So it's tricky to ensure it's impossible, but you can reduce the ways.
The hard bit is making it impossible for you yourself, because whatever you can remove you can also add back. I can uninstall YouTube from my phone (I am rooted), but can also install it in a few seconds. So if, as I infer, that is your concern then it will be very difficult to achieve that.