It is contested to some extent as well, but it's generally a good deal more accepted because it's not nearly as much of a misnomer. For one thing, the geographical tag makes it much, much less misleading than in the case of the aftermath of the western Roman Empire: calling that economic downturn "the Dark Age" is actively misleading, because it's an attempt to suggest that it affected all of Europe (something you, too, seem to think, and which is absolutely unequivocally false), or even the whole world. The specificity of "the Greek dark age" is a fairly strong defence.

It's also not as misleading in terms of availability of primary sources. In the post-Roman case, people kept on reading and writing texts, and we have a goodly number of writings from that period -- more than we have from some phases of the western Roman Empire, in fact. In the case of the Greek dark age we have absolutely nothing at all.

In terms of cultural and practical innovation, "the Greek dark age" is somewhat misleading, as is "the Dark Age", but even there it's not quite as misleading. It used to be thought in some circles that the Mycenaean collapse was the end of a pre-Greek civilisation, and that Greek culture sprang up only afterwards. We now know that that isn't true. But all the same, it is hard to find more than traces of continuity, other than in language. An awful lot of cultural heritage, infrastructure, and expertise was destroyed for good.

As long as we recognise that there's no such thing as an age where people weren't innovating and creating as hard as they could go, and that the term really reflects economic and social constraints on cultural productivity rather than a lack of productivity, I'd say the term is not too awful. There will certainly be people who mind it, and I have no argument with them; I agree with them there's always a danger of reading a phrase like "dark age" without nuance. But in this case I don't think it's worth getting too het up over it.