Well, as this thread now seems to be more about boxes than fiddling, can I first say that the old quote from JK was very much tongue-in-cheek and should be seen as such, though there are some of the “semi-tone system” players where the left hand does just “flap in the breeze” rather than seem to hit any specific chords.
Speaking as a B/C player, a popular misconception held by those who don’t know is that we would only play tunes in B and C: of course that is rubbish, and we usually play in the same keys as anyone else, G, D and A being the most popular majors and E, B and A being the most often-played minors. As far as the left hand goes with just 8 buttons, I have Gs on both pull and push, D both ways also, C, F, A and E and a stop to take out the thirds so that a “chord” can be major or minor. The one chord I don’t have, which could be useful for tunes in D is a Bm. And, being fully chromatic, there are plenty of interesting right hand chords to find, such as A maj, Bb maj, Emaj and min, C#min. Playing in C is actually a bit of a faff, as it entails a lot of pushing and pulling! Need I go on? I don’t know for sure, but am told that the C#/D is even more versatile.