I don't think that concertinist is a 'proper' word; concertina player, well hopefully. Certainly something to aspire to.
Does this mean you also prefer "organ player" to "organist", "guitar player" to "guitarist", "violin player" to "violinist", etc., etc., etc. ?
I would think the opposite, that the "-ist" suffix suggests more status, as in "X is only a piano player, but Y is a pianist".
Or maybe you think it pretentious ? I will admit that it does have rather an "old-fashioned" ring to it, but perhaps that is because of the lowly status our beloved instrument is perceived as having.
P.S. Thinking some more about this, most of us probably come to the concertina via folk music, in which case we would probably say "guitar player", rather than "guitarist", and even "fiddler", rather than "violin player", never mind "violinist".
In which case, given that our chosen instrument is often referred to as a "squeezebox" (or a "squashbox" in Zululand), and the Irish preference to descrbe a button accordion (and sometimes, by extension, a concertina) as a "box", or an "accordionist" as a "box player", maybe we should all be known as "boxers", and not just Jim (the Heavyweight Champion of us all) ?
Of course, there is always "boxist" as an alternative, but I don't think it would win many votes.
Edited to add Postscript.
Edited by Stephen Chambers, 22 February 2004 - 09:31 PM.