By this point, it's a solid part of our cultural heritage. It's not that it's no longer appropriate to use it, it's that anyone who reaches for it needs to be aware of its history and context. I wrote a mini-essay about what Terry Pratchett did right in this regard that you might be interested in.
(Of course, First Girl stories and Girl In Disguise stories are not quite this same thing, although there is significant overlap, c.f. Alanna, and the same thing applies to both of them.)
What Pratchett did is what normally happens to tropes like this - they become part of the cultural background and people start to send them up and subvert them. It's the natural life-cycle of a trope, and we're well into that portion of it, so anyone who writes a straight-up FGE/GID story is naturally going to seem a little old-fashioned. Still, that doesn't mean it can't be part of a good story.
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(Of course, First Girl stories and Girl In Disguise stories are not quite this same thing, although there is significant overlap, c.f. Alanna, and the same thing applies to both of them.)
What Pratchett did is what normally happens to tropes like this - they become part of the cultural background and people start to send them up and subvert them. It's the natural life-cycle of a trope, and we're well into that portion of it, so anyone who writes a straight-up FGE/GID story is naturally going to seem a little old-fashioned. Still, that doesn't mean it can't be part of a good story.