When would you do this? Are you talking about playing solo, in a band, accompanying yourself singing, or something else? Are you actually going to play these *as* chords, or just use them one at a time as part of a bass line?
I mean, there are no absolute rules in music, and if you personally love the sound of an open G chord strummed on a bass, that's fine, but most people in most contexts would say that sound is kind of awful. Low notes played together are very muddy.
A lot of the time, the typical bass "chord" is two, maybe three notes, played up in the high-numbered frets.
E.g., one finger on the E string 15th fret, one on the G string 16th fret, and you've got a nice-sounding G major. Shift that up and down and, boom, now you can play all the major chords.
But I don't know if that's what you're looking for.