In Europe with soccer you don't really see retired numbers but certain numbers for certain teams hold special significance. Usually, those numbers are reserved for players who have established themselves and earned the right to carry on the tradition associated with that number. Granted, for the longest time, numbers were assigned to positions, not individual players (probably explains why it has evolved differently today where you don't see retired numbers).
Still, I think something like that could work. Where a player could establish themselves after few years and then, if they wanted, they could switch to that reserved number. For instance, I look at the number 36 and remember elite safety play, having grown up watching Leroy Butler and later Nick Collins hold that number for much of my lifetime. You could take that number and only give it to safeties (or maybe more broadly defensive backs) that have established themselves as great players. That way, you honor the player(s) that have established a great history with that number, but it is still available for use going forward.
Born and bred a cheesehead