The AP's make rather good sense to me, and are quite well suited for deciding the startig times, as well as the ties.
At competitions, people often need to determine their starting time - for example they want to coach each other in a team, or they want to focus on a certain discipline, or they want to take a nap or something to eat between disciplines, or they need to catch a train before the competition is fully over, etc. etc. It is very useful, I am am glad this possibility is there. I see no reason why it should not be possible. People use it frequently to everyones satisfaction, and I did not meet yet any competitor who would be unhappy that he can influence the starting time. You are the first exception.
Now, of course you can tell competitors can chose their top time without any AP. But then everyone will run for the best strategic times without any risk. Currently, with the AP, you risk either too low AP (hence a loss in case of a tie), or a too high AP (and hence a penalty), so you have to choose your time carefully, which makes it definitely more just for everyone, and it assures easier distribution of the starting times.
Or you can decide the top times randomly, but it will be a great hassle for most of the competitors without any real reason. And you may influence the results unjustly. Having to risk to get a strategic time is much more just on my mind. Being appointed to the best strategic time is unjust, and may also allow the organzier manipulating the outcome, so that their friends will profit.
The only way that would make sense and be just in the same time, would be basing the starting times on the current ranking (FIPSAS in Italy has such system for the "elite" category), but then again you need an up-to-date reliable ranking for that. We do not have any complete ranking, since organizers usually don't send any results from competitions, or send them months late. And you as a competitor would not have any choice of the top time, so it would unnecessarily complicate the competitions to many. It would be fine and acceptbale in a professional sport, but it would be a great hassle for those who travel from far, and those who can't come with their coaches, and need to rely on buddies, or adjust their start times to the travel times.
Highest AP's at the beginning? Sorry, but that does not make any sense to me at all.