I'm more interested in this from a technical / networking perspective. It sounds nice on paper, but realistically, is very challenging to implement.
The original proposition of the ghost time being sent to the server when the game is paused, this just isn't feasible in a race scenario. PayDay2 has a similar feature, when a new player joins, the game suspends on the server while it integrates them into the madness and downloads all the information it needs from them. Games never have more than 4 human players in PayDay2, and the action isn't nearly as fast as GRIP, so it's fine here. However, this would be highly disruptive in a race, so isn't something I would advocate.
The other main solution is of course to have a dedicated server, and have each racer, as part of the loading process, upload their best timed lap for that track to the server, which is then processed concurrently as a phantom vehicle, which instantly takes over at the right point in the race (according to the race clock). Issues with this are track position differences, velocity differences, item pickup differences, and differences in positioning and velocity of all other participants, not to mention a potential plethora of weapons being deployed and coming to get you. Oh, and needing dedicated servers as well. And that these servers would need to analyse each racer's replay to calculate optimal pathing for the lap, and be hot-linked into the control of that player's vehicle. And having the AI core loaded at all times.
Technologically speaking, this is a highly impractical endeavour without serious time being put into developing an efficient server core and running it on dedicated hardware, or ensuring that PtP game hosting runs on a host with a strong connection (say, 10 down and 5 up minimum) to reduce overall wait times when synchronising all this information, both before the race starts, and during the race.
Just to clarify, I really like the idea, but the scope of something like this is enormous, so it's very unlikely to happen at this time (IMHO)
"Tired are we, the few who battle endlessly, against the never ceasing sound, of inevitability..."