Hmm..as SharonA says the fact that low E is open stringed(in a C chord) may allow it to ring out and have more presence--and not an attractive presence. It does sound better to my ear when I rest my picking hand's palm on the E string to prevent it ringing.

But the low E sounds more interesting when it's used sparingly with other bass notes in a strum:

using the C chord:
C(5th string),then strum;
G(6th string),then strum;
E(open 6th string) etc;
G(6th string)strum.....

Here, the E is a passing tone, as MidChuck says. That seems to make it more palatable.