Excellent question, Dave.

The reason is that playing the "fifth" as the lowest note of a chord, e.g. E for the A chords you mention, is considered awkward in most situations (second inversion), in particular at the end of a song. In some situations, however, it is tolerable, for example when followed by an E major chord in your case. But then the empty A string is best omitted, which is difficult if you are strumming through.

Guitar strummers are often unaware of the beauties of a consistent bass line and other subtleties of counterpoint, which is a bit of a shame. If you are lucky, you have a bass guitar or double bass "below" you.