Our kids are the big users of the YouTube app, honestly. They've got a bunch of their little cartoons and "how to" videos bookmarked in it as favorites and so on.
But even they've complained that the app is flaky. On my Sprint iPhone 4s, for example, my kid often has to power the phone completely off and back on again before the YouTube app will stream any videos when we get to my mom's house and it connects via her wi-fi. It's weird because everything else that uses the wi-fi on the phone seems to be fine when this happens, so I can't really blame anything other than the YouTube app.
I won't mourn its loss if Apple deletes it. But I agree that A) Google would be wise to release an enhanced, new YouTube player app in the App Store as a free download for people who still want it, and B) it might be nice for Apple to at least provide a shortcut icon that launches the m.youtube.com site in Safari on iOS devices.