Have had this problem since I first got it. The error message, when I get one, says that your browser doesn't support this mode.
Other browsers work fine, at least Puffin does. Puffin is my go to when safari doesn't work, like when you're in Lagos, Nigeria. It's (Puffin) a life saver.
Full screen YouTube in most third party iOS Web browsers, even ones where you can change to either that desktop Website of YouTube or change the browser to be recognised as another popular Web browser, will NOT allow full screen YouTube.
Have you tried using the YouTube app, instead, which allows full screen video playback.
Well, I was having a great deal of trouble with all ways, but now, the app, and safari are allowing full screen as well as 3rd party browsers. The only thing that I can attribute to the change is having the associated iMac safari browser replicate Microsoft Edge, with the Develop menu.
FYI
Puffin Web browser will always work as that Web browser is redirected to online servers, that serve tbe Web browser, to stream the actual desktop website content from other unknown remote server locations.
This is how Puffin is able to stream most Adobe Flash Player content through iOS.
It is actually streaming a desktop version of a web browser with Flash Player installed and is transmitting this content through remote servers to iOS devices.
The issues come from where the original content is coming from as Puffin gets its content from other online servers with unknown security.
Puffin claims that their transmitted Adobe Flash Player content is secure, but I have been always dubious of that claim.
Puffin Web browser has been around for nearly 9 years, or so, and I have never used it or trusted its claims.
Puffin worked when sarfai and the YouTube app didn't.
iPad pro safari is not able to display youtube in full screen.
