Geordi's problem was never his eyes alone though - it was also or primarily his optic nerves and the DNA of both. We know this from All Good Things... where they talk about the DNA in his optic nerves changing and this fixing his problem.
It's also established as genetic in The Masterpiece Society, where Geordi asserts he'd have been terminated as a single cell (and is not contradicted), which is only a viable claim if his condition was genetic.
So actually, I have to give this one to Strange New Worlds, not to the pedants (who am I often among). I think they're okay to have an eye-regenerator, because it wouldn't work on Geordi beyond regenerating his non-functional eyes and non-functional optic nerves. So if Geordi lost his eyes, sure they could get them back, but they still wouldn't work - they never worked, and they don't because of his genetics.
EDIT - Looking into this, this is further supported because the videogame Star Trek: The Next Generation - The Transinium Challenge which came out in 1989 also said his blindness was caused by an "incurable optical nerve defect". That game wasn't canon BUT it was heavily derived from the series bible and from the people who made it asking questions of the writers, so I think it's safe to say the "optical nerve defect" thing was something the writers considered to be the case from early on, even if it never made a script until All Good Things....
Also, let me say - somehow I knew this in the early 1990s, before All Good Things... came out, so I suspect it was something that a Trek writer had mentioned to a Trek zine which I read when I could get them (which I used to read, yes I know, I know - some of them were amazing though - but I couldn't get them much in the UK), or which had been discussed by one online or the like (unless there is another episode where it's mentioned - Memory Alpha is surprisingly useless here, essentially glossing over his blindness).
