The problem I described would arise when someone who does not know about GADTs and type inference accidentally writes a GADT. But this cannot happen easily today, precisely because of the need to write the extension.
This is not a very believable objection in my opinion. GADTs are guarded by a different syntax which isn't used by someone who doesn't know about GADTs. So writing a GADT by accident is exceedingly unlikely. Besides, Ocaml has GADTs by default (with a similar syntax split as Haskell's). I don't believe I've ever heard anybody complain about GADTs since they've landed, certainly of anybody writing one by mistake.