Allow Black to choose White's first move. They aren't allowed to pick f3 (huh, looks like Stockfish greatly prefers f3 to g4)
Or more, based on https://lichess.org/analysis you'd have to ban a couple more moves like a4/h4, but you could opt to restrict picking first moves within Stockfish range at some depth of -0.1 to 0.1 (looks like c4 is enough to be 0.1 at depth 47)
This may increase the draw rate
If you want to keep engine analysis out of the rules, you can go the "evenly split candy between siblings" route: after White's first move & before Black's response, Black may elect to trade positions
Yes, but it'll get _much_ closer to 0 than e4 or d4, which are already close enough to 0 to produce good games won by black. I wouldn't call it needlessly unfair
It also means White still gets the edge of being able to prepare for the first move vs their opponent, ie they may've studied 1.Nc3 lines much deeper in preparation, whereas currently White gets the edge of choosing the first move & it's advantage
ie White gets to decide whether they prefer their e4 prep or d4 prep against their opponent's prep as Black, so if White doesn't want to play against their opponent's Sicilian they play d4. This is a theoretically moot but real advantage. See Fischer's performance with c4: https://www.chessgames.com/perl/explorer?pid=19233&side=whit...
See also how well 1.g3 or 1.b3 have performed while Stockfish gives both a solid 0 eval
In short, while I started with Yes, I mean No. Because b3/g3 are equal enough that White gets an edge by deciding whether the game will be a g3 or a b3 game
Or more, based on https://lichess.org/analysis you'd have to ban a couple more moves like a4/h4, but you could opt to restrict picking first moves within Stockfish range at some depth of -0.1 to 0.1 (looks like c4 is enough to be 0.1 at depth 47)
This may increase the draw rate
If you want to keep engine analysis out of the rules, you can go the "evenly split candy between siblings" route: after White's first move & before Black's response, Black may elect to trade positions