I think it's a misconception that the nut slot for a low G string would be deeper than for a high G. The bottom of the slot should be rounded, so that even if you did swap a low G for a much thinner high G string, it would still have the same clearance over the first fret. And while I've not swapped the G string on my Blackbird Farallon from the low G it came with, I can see that the nut slot is indeed rounded at the bottom. So all should be good.
However, if the slot is cut with a V shaped file, then using a more narrow string would allow it to drop in the slot, possibly leading to buzzing. Which is why you should NEVER use a triangle file on nut slots.