I suppose the topic begs the question: if this is a problem... should something be done and if so what?

I don't think this problem merits any action.
What's gonna happen, people who have never played healer before will gear up and head straight into EXes, turning them into trap parties?
So what?
Not only do I not see new healers charging headlong into stiff content if only because healers have their own version of tanxiety.
I don't think there would be some kind of harrowing surge of shitty sages because of this.
There might be bad healers, but I don't think this will contribute to that to any long term or significant degree.

But either way, what would SQEX do? Ask healers to prove that they're capable of performing their job before allowing them into content?
IIRC they've expressed they don't take to this idea. Someone asked Yoshi-P in an interview if they'll ever consider locking access to raids behind clearing it's training dummy, and he said no.