A bit off-topic but perhaps interesting for a different perspective on a similar theme: many years ago when I lived up in northern VA for a while, the BMWCCA “HPDE's” were really just time trials, at least with the National Capital Chapter up at Summit Point. For the weekday track events when the hard core guys would take off work and show up, we used to divide up the whole group into 3 driver teams for an end of the day "tag team" competition. We used the lap times (best for each person) and tried to form teams as close to the same total time as possible. Slower teams got a break on the start by being able to leave early similar to bracket racing.
It worked like this:
-- standing start at pit out; two cars from two different teams side-by-side
-- your next in line teammate moved to the start behind you once you left
-- you had to make one lap of the track and stop up to but not after the start/finish line
-- you unbuckle, jump out, and run to the pit and tag the trunk of your teammate's car
-- process repeats until the final group has a running finish, first team across wins.
Yes, you can imagine the opportunity for people to fall, make stupid decisions and get hit, crash from trying so hard, whatever, but DAMN it sure as hell was fun! At least in all of the events I was involved in, there was never an incident of any kind (fortunately in retrospect).
Between stuff like the above and the autocross-time-trial-like nature of track events, I'm sure we contributed to today's strict insurance regs for "driver's schools".
Sorry for the aside...just an old story I thought I would tell (before I can't remember stuff like this any longer

). Clearly something similar in an autox is not workable due to too many drivers, but perhaps the outline of this experience will spark some folk's imagination.
Chuck