I think that FP works fairly well as it is; however, I would like to see them stop accepting them late, unless an event that can be confirmed has occurred.
For example:
You have a FP for Star Tours and go to ride the Matterhorn, the Matterhorn breaks down and you are stuck on it. You have an ADR at 5:00, you FP ended at 4:20, you would have had enough time to go, but now you have to go to dinner first. They should have a list of all attractions that have broken down that day at each FP return lane and if the story checks out (you explain the above situation), then the FP is accepted late, if not, then it would not be.
The exception to this should be for those with GAC cards/wheelchairs/canes/walkers, FPs should be accepted anytime after the start time. There are a lot of things that can happen that can make it difficult for those with special needs to return within the specified time frame. I think they should also be able to get FPs for all attractions that they are planning to do at once at a special machine (spaced out throughout the day according to projected crowds), but that is another story.
Out here we don't have FPs for any shows (except WOC, which noone can use the viewing area without one).