I also wouldn't play a blues A7 D7 and E7

I'd play A major (with occasional 6ths and 7ths) D (same) and then either E7 or E (same). I suspect it's because the blues scale is not the same as the normal scale. Certainly a blues harmonica has different notes in from a non-blues harmonica over the same nominal root, and I think the cross is different too isn't it?