Saturn era first party Sega racing games tended to have an option called "Time Lag" for vs play. It gave you a time limit, adjustable between 1 and 8 seconds, of how long a player had to pass a checkpoint or start/finish after the other player. This time does not adjust or accumulate, so all that matters is the gap between both players. There's no other end condition for the race.
If both players are at a similar skill level, and high enough to mostly stay off the wall, this can become a very intense endurance session where consistency matters just as much as speed. This is the kind of battle I crave.
I don't think this exists in anything remotely modern? Though to be fair I'm a bit detached from newer games. When someone corrects me in the comments, there will be a lil edit right below here.
