Most chord diagrams assume the chord will be strummed using a downstroke. So, as Grishka says, the Low E as the bass note sounds awkward. But, and this is a big but, if you play that same A chord using an upstroke, that open low E sounds just fine as the final note. And if you fingerpick and incorporate the low E into picking patterns, it also sounds fine.

BTW, I've never had any problem with the sound of the low E as bass note in an A minor chord, just A major.

The usual disclaimers (YMMV etc.) may apply