I've been trying to find a work around this... not too much luck, but there is a way if in a desperate situation:
Services such as PWNYOUTUBE (deturl.com) automate links which provide you with an option to download the youtube video straight from the server in flv format and for mp4 format... clicking the latter allows one to view the video on the iPhone (higher quality... might not work so well on EDGE)....
Of course this means finding the video you want, figuring out the URL (mobile YouTube.com vs. the mobile app is already painful) then to copy the URL, either add PWN in front (or paste it into deturl.com) .... by the time you get this working, you don't even care about the video anymore.
They wouldn't want you to play their videos on the phone (or embedded on another page) since that would bypass advertising (lots more of that on YouTube these days.) but I understand that they don't want to A: put ads on the iPhone app, and B: lose advertising....
I'm not a programmer, and would love it if someone knows of an easier way to automate this, since I have a series on YouTube I regularly watch and would just love to enjoy it with the rest of my podcasts and video entertainment: on my iPhone... I'm sure a webapp would be able to do it (maybe a bookmarklette?) but so far, I haven't found anything