As someone who has been involved in organizing and putting on track meets at multiple levels the changing start lines are only an issue when the timers and the starter are struggling. I think it would cause many more problems at the dual meet level (or at a poorly managed invitational) than it would at a well run meet like Arcadia or a state championship. Considering the typical meet schedule where the 3200 follows the 200 adding a 3000 would not even add an additional start line move.
I am personally have no problem with the 1600 and 3200 meter distances but that may be a product of growing up in an era and location where they were the norm. However, at the middle school level (USATF Junior Olympics) I ran the 1500 and 3000 and there were no issues there either. I think the lack of consistency between different states and different levels of competition can be confusing for the athletes when they are trying to compare times with their peers or with old records from bygone eras.
The 5000/10000 would be a bad idea as standard HS distances. As many posters have mentioned they would add a huge amount of time to already long meets. I have to say that even as a former 3200 guy it is pretty brutal to have to watch kids running 15 minute 3200s at a dual meet. Imagine that 15 minute 3200 athlete in a 5000, let alone a 10000. Cross country is different because there are fewer races to complete in a given meet and spectators are there specifically to watch a distance running event. All that being said, the 5000 is a great event at the HS level under specific circumstances. I ran in one of the two editions of the 5000 at Arcadia and it was an incredible experience. I believe that the fans enjoyed it as much as the athletes based on the noise level during the race. In a setting where it brings together a group of talented kids who are going to run fast and be competitive the 5000 is great, but not at most meets.