I've played for well over thirty years and have never really used anything other than standard tuning. I have used Drop D for a few traditional tunes and experimented with open tunings for slide. Frankly though, I just find other tunings too confusing. I would certainly use an alternative tuning if I wanted to learn something that needed that tuning but I wouldn't use it otherwise. Some payers, though, use different tunings and produce marvellous work beyond anything I could even dream of.
Some tunes need a different tuning - I've been listening to Leo Kottke lately and most of his tunes couldn't be played in standard tuning. Here, the tune would dictate the tuning. If Kottke played it in Open G, then use Open G.
Some players have an alternative tuning that they favour for just about everything (Richie Havens, Keith Richard etc.). These people treat that tuning as their "standard".
A few players change tuning for almost every song. These people seem to do it naturally, and I don't know how they decide on which tuning to use.
With the example you give, I'd just use standard tuning (like EC). Using an open major tuning can make it difficult to find minor chords and I wouldn't want the main chord (the G) to consist of all open strings, it would just feel wrong to me.