I think it's interesting to ask where the concertina can fit today. For instance, is there any room for the concertina in bluegrass music?
I've thought about this a lot too. Apart from Irish I play South African jive and the standard repertoire of hymns, Morris dances and sea shantys. I reckon that old timey would be the best bet. I think a concertina playing fiddle parts would fit just fine.
I've read that Cajun music was more harmonically diverse before the Cajun accordion (1-row melodeon in C major) became popular. I suspect that bluegrass is also a bit too harmonically diverse, seeing as how it's so string-centric.
That shouldn't be a problem for 3-row anglo players although, since I have a 32 button instrument, I tend to think of it as more chromatic than it really is for most players. I'm pretty comfortable in about half a dozen major keys at least and can play obligatos to singers in any key, although I have to practice up for remote keys. Basic boom chuck accompaniment isn't very easy in distant keys.