Years of fingerpicking stick to a fellow. I generally play a 3 fingered A Major UNLESS I want a walking bass. Then I’ll barre the 3 strings with my index finger and my ring finger is available to hit the 5th and 4th strings at the 4th fret as needed. And if I’m feeling bluesy I can use my pinky on the 4th string/5th fret as needed also.
Oh, and for Alice’s Restaurant Massacree, you need to barre the A Major so you can do the pinky stretch needed for the “… you want at …” phrase. On the other hand, if you play any early James Taylor stuff, his signature is A Major with an open 2nd string which he’ll play and then hammer on at the 2nd fret. Of course, he does an odd fingering for that A; as if he’s playing an A minor with his index finger scrunched up to the 2nd fret with the other 2 fingers.
The 234 G Major frees up your index finger if you want a G Sus 4 or want to pick some melody notes and it’s easier to change to or from a C Major (especially a C/G) or G7.
We used to call the 4 finger G Major a “Country G”. I don’t know why. It’s got a modal sound because the only 3rd is in the 5th string. The ring finger/ 2nd string / 3rd fret is a good pivot if you’re changing to or from a D Major or Minor. And IMHO, the 4 finger G Major is the only G Major that works well with “You’ve Got To Hide Your Love Away”.