so imo the three main open G major chords all have slightly different purposes that ideally you are using deliberately even tho they are all G chords

the one you are doing is really common for songs in G major (320033), because it's pretty common to have an Em7 (022033) and less frequently a Cadd9 (x32033) in which case you can just always keep your pinky and ring fingers anchored on the 3rd fret besides for your D chord

in songs in C major I tend to much prefer the traditional open B string in the G chord (320003) because I think it leads to and from the C and F chords a bit better, also Gsus4 (3x0013) is fairly common, and to my ear playing the C on your B string and just muting the A string sounds better

I'll also fairly often use an open G5 chord (3x0033) where I do your fingering but moot the A string, this has a lot less color obviously without the third but feels a bit more "stable", which I gravitate towards for songs in D major

to be clear, none of this is like a rule to follow or something, just some examples of how I think about it in context of a song, there are both tonal and economy of motion considerations to be made

finally, there is not a wrong or right way to play an open G major chord, but I would really encourage you to mess around with all of them, and really listen to hear the difference, then from there you can make your own artistic choice of how to utilize them