But sure, if you do it on purpose because you think it helps, by all means, move however you want. We will do our best to track you.
I'm mainly thinking of unconscious moving. But sure, if you are nervous due to the huge audience, you will think of other things and not that - which is why we don't approach speakers about this before their talk.
You'd think this could be solved with the proper zoom angle but then the pros get on your case with too much headspace, unfavorable body cut lines and never forget to never film the audience.
I just talked to a speaker for tomorrow who, from the video material, assumed they'd be talking in front of maybe a hundred people. They're scheduled for room B which holds about 2000 and got a shock.. so the dimensions look quite different on the stream.
The issue can be mitigated by a better filming crew really. The mixer is really important for coordinating (when the cameras do random stuff once in a while you probably have a inexperienced mixer who uses the intercom too little). It's possible to follow the speaker well enough if the mixer gives breaks and the camera tripod settings are right for you. Special cases get an experienced crew.
Not sure about the stage fright. I think it depends on the details actually, but I'm still working on that too.
A guide would be good though. I'll suggest it further.