Hey, I don't own this game, but I watch a couple of youtubers who play this game a lot and there is one thing they seem to struggle with:

If you have enough great people points to obtain a great person and one or more other (AI) players do as well or are close, but the current great person on offer is not the one you want, you can choose to skip the current great person, however this means that often another player will take it and one or two other great people in the same pool will get sniped by other players, while you haven't been given a chance to look at them. This is very frustrating, because you, who has

To fix this, one thing that might be possible to do, would be to always give the person with the most great people points (left) the first pick at a new great person whenever a great person is picked up by a player.

Otherwise, perhaps something along the lines of this mod could be done: make the new great person in that pool 10x as expensive until the player with the most points (or the player who first skipped the previous great person) gets their turn.

Is any of this feasible?
Would it actually be fair?

Another alternative:
Let only 1 great person be "claimable" per turn. Let all players either claim it or not claim it, then at the end of everyone's turn, the person with the most points gets it. I guess this wouldn't be very compatible with faith- or gold-buying great people, though?