Forcing certain players to "play the game it's meant to be played" is perhaps acceptable when it's needed to gather some extra information about their playstyle etc., but not beyond that. In my eyes it's not a solution, it's kinda unfair to the restricted players. You can test it on yourself freely - either using AdminEFR or if you have balls to do it without EFR.
Anyway, we're not really debating that "how RACE should be played", we're rather debating that players are annoyed when people wait at the end for no reason, right? In non-trials RACE maps, I generally don't see a reason and always abused (pushed their nitro) - it's really just annoyance.
In trials I can understand that more players want to finish the map. Reading through this topic, what I would say is sometimes indeed the player at the objective is waiting for another player to finish in a good will and other times there is one player at the end without really waiting for anyone, just watching the others to try and fail (and ragequit because of boredom).
Problem with the prompt will definitely be - I'm sure some of you remember Bono's rage on RacewayAlpha

- that either it will disctract you from driving (like midgame voting) or it will go kinda unnoticed. I don't know how much has been implemented here (or elsewhere), but:
1) In AS, not doing the objective when you can is considered team hamper and a bannable offecne. I don't see why in RACE such couldn't be seen as an annoyance.
2) In trial maps, completing the objective would not end the game right away, but set the clock to, say 3 minutes, for other players to finish (with Aza's checkpoint system, the timer would run only if there is any other player advanced enough). Waiting before the objective (so this timer isn't triggered) is 1).