Just to avoid confusion, can you tell me what you mean with profile in this case? Are we talking about for example Android phones which have this feature in some cases to 'distinguish' between a personal and work profile?
You may want to approach this the other way around. Instead of "blocking personal devices", only allowing "managed/compliant devices". Effectively it would be the same.
I do not recall seeing the possibility to actually block setting up e-mail, unless you do this per user or do it the other way around - make everything that should be allowed compliant and block everything else. Perhaps someone else has more insight into this specifically.