Not all D/G boxes have accidentals; and even if they do, the standard D/G box has only the 8 basses, limiting the keys somewhat. Sure, you can find workarounds using chords on the right hand side, and/or simply leaving certain notes out of chords or phrases, or playing an almost-OK chord that more or less works, but it's not an obvious choice of instrument if you intend to stray from its basic keys.

Yes, Rowan, it's an international forum and usage does vary. We all learn to make allowances for this. In England, I've never ever heard a two- or three-row diatonic box referred to as a "button accordion". If you must have a "known authority" to support this usage, the big folk-music specialist shops (eg Hobgoblin and The Music Room) refer to these as "melodeons" and the ones with piano keys as "piano accordions". This may well be relatively recent terminology, and it wouldn't surprise me to discover that it only goes back 40 or 50 years, but that's certainly how the names are used by session players across the south of England today. If you go to a festival or event anywhere in England advertising a "melodeon" workshop, the standard instrument used will be a D/G box. Single-row boxes in C or G are still around some places, but they're a bit of a specialist, minority thing.

I made it clear enough how I was defining my terms, and I'm simply using the words as I hear them used consistently in England.

Marje