I started by saying that eliminating FP+ and only having one line wouldn’t work. GAC works with the FP+ lines and therefore has nothing to do with the discussion at hand. If the only available line has a wait of 40+ minutes, a GAC doesn’t help.
So, firstly, yes, getting rid of FP entirely for GE would be the best way to solve this situation regarding queuing. Let's get that out of the way. The way queuing gets supremely worse with FP is because of the merging of two separate lines and having a ratio that dictates FP going majority, standby second (the 3:1 ratio that is applied to attractions; whether or not it works for each one is a different story for another time). It would have everyone on the same playing field and make the lines shorter. As someone else has said, some attractions have benefited from having FP (basically those who have dual loading platforms, ie, SM, Star Tours, Dinosaur, etc), others have had it destroy their already efficient queues (Peter Pan, SSE, HM, etc). One only needs to look at how TSM in Disneyland was before they introduced FP only a few years ago compared to the lines for it at DHS and that was without a third track.
Now, as for the actual bit you're talking about, you're acting as if no attractions have accessibility access. Since the ADA act was put into place, all attractions, no matter what age, have to made reasonable accommadations for those with disabilities. The GAC was a good, but flawed system in many ways. The new DAS system is much better in many aspects. You get the time that's assigned to you determined by the countering of the standby wait and the whole group goes up the FP line. Bam. Simple. You don't have to wait in standby at all, you can go do anything you want and return at whenever.
How did the HP attractions handle it with no Express access for the first several years? The same way GE could do it: by only having standby for everyone and when it comes to folks that need accessbility access, they have their assistance pass, they get a return time and when it was time, they entered the attraction via the already built but unused Express lane, thereby having limited to no wait.
Tl:dr: As someone who had worked in Attractions at WDW for 7 years, every attraction at every park in the country (and presumably the world) has their own way of including disability access. Just have to do your homework.