So I understand the idea behind this but strongly disagree. This proposal fundamentally changes FMC as an event. Why? Here's a hypothetical =>
There are 2 competitors (1) Jerry and (2) Terry
Jerry and Terry both get a final solution of 24 moves. Both Jerry and Terry find their 24 move solution in 20 minutes. Jerry feeling that he has found the best solution submits it. Terry on the other hand feels that there is a better possible solution. In this case we KNOW that there is a better solution as neither of the solutions are optimal, given God's Number. Terry spends the remainer of his time looking for a better solution but is unable to find one. In this scenario Terry is punished for looking for a more optimal solution.
So why is this unfair? I said earlier, this proposal, within this specific scenario, changes the event from FMC to Speed FMC - these are NOT this same event. Changing the parameters of the event, in a case of a tie, specifically on the terms of time doesn't make sense considering that the entire event is NOT based on time.
A possible better solution would be to measure each solution in both HTM and QTM (or some other turn metric). In this case the winner is rewarded for have an overall more efficient solution - the tie breaker is now based in the parameters of the event - efficiency. This, however, doesn't really work. Here is another hypothetical =>
Again, there are 2 competitors (1) Jerry and (2) Terry
Jerry is a newer competitor in FMC and, as such, uses blockbuilding to reach his solution. Terry on the other is more experienced and uses DR. As in the last scenario both Jerry and Terry reach a final solution of 24 moves. To break the tie between the two we use QTM to find the overall more optimal solution. Here, because Terry uses DR there is a bias towards using double turns and thus Terry loses the tie breaker. This creates a problem where different method/approaches to solving FMC have an advantage - here Terry is punished for using DR which isn't fair to them. The same thing happens if we use other turn metrics to determine the tie breaker. If Terry were to instead use Corners First there now is a bais as the method tends to utilies more slice moves. One way around it could be to compare the solutions with multiple turn metrics, say HTM, QTM, and STM. This helps to smooth things out as to remove some bias but the bias will still exist. The other problem you run into is solutions which are identical - there doesn't exist any metric which breaks the tie (this happens more now than ever with DR as solution tend to be more linear).
Phew, that was a lot but we're not quite done. I am now going to compare this to a different event - 3x3. I will say that this isn't one to one so take this with a grain of salt. That being said I do think that this will at least make my position a bit clearer. Here's the final hypothetical =>
There are 2 competitors (1) Vinnie and (2) Winnie (RIP Jerry and Terry - you will be missed)
Vinnie and Winnie tie with an average or 10 seconds.
Vinnie's times are 8, 12, 10, (7), and (15)
Winnie's times are 9, 10, 11, (8), and (12)
On average Vinnie uses 12 seconds to inspect their cube
On average Winnie uses 8 seconds to inspect their cube
As a parallel to the above proposal, the tie breaker is determined by the time to submit. The lower the average inspection time the lower the time to submit. Winnie wins the tie breaker. Again this funimentally changes the event in the case of a tie. We move from Ao5 with standard 15 second inspection time to Ao5 with 0 seconds of inspection time. These aren't the same event. Again the parameters of the event become fundamentally different. All of a suden something that does not at all counted against you is counted against you, in the case of a tie breaker.
So what is the solution? Well, the more equitable solution would be to extend the parameters of the even which is the best average time. In this case we take the Ao5 without the removal of best and worst times. Vinnie has an average time of 10 seconds and Winnie has a average time of 10.4 seconds. Vinnie loses the tie breaker. Here Winnie is rewarded with being more consistent - which is the entire idea behind the event - best overall average.
Now, there is another possible sotion to a tie breaker - best single. In this case Vinnie would win the tie breaker with a fastest time of 8 seconds. Although is works we again break the rules of the event. An Ao5 shouldn't be determined by singles - it should be determined by average.
Okay, we're at the final stretch. Up until this point, when comairing FMC tie breakers, we have compared ties with SINGLE solutions. But wait, what about averages? Good point. Here out final hypothetical =>
There are 2 competitors (1) Jerry and (2) Terry (welcome back kings/queens)
Both Jerry and Terry have a average of 25
Jerry's solutions are 25, 20, and 30
Terry's solutions are 35, 18, and 22
Just as before we have our 2 possible solutions (1) Average solution length with average solution time and (2) Average solution length in multiple turn metrics. As before I believe sotution (2) is better although it will still run into the same problems. However, if we look back on our 3x3 section we have a secret 3rd solution being that the competitor with the lowest single would win the tiebreaker. Here, Terry would win the tiebreaker. This however still runs into the same problem - the metric we are looking for is the average solution. In this case Jerry is punished even though he is more consistent. Given this, our last and final solution, would be to compare the distance between the best and worst solution. In this case Jerry would win the tie breaker with a difference of 10 moves between their best and worst solutions where Terry would lose with a difference of 17 moves between their best and worst solutions. Here Jerry is rewarded for being more consistent which lines up more with comaring averages. Not perfect but definitely better than the other solutions, imo.
I think that's all of my thoughts on the matter. If there's anything that I can clarify please lmk, as I understand this is a lot to take in all at once and is relatively complicated.