In a complex system, variables don't react in a neat and orderly fashion. Adding the LMA theater with a capacity of 5000 doesn't draw 500 people from Rise, 500 from Slinky, 500 from Star Tours, etc. It doesn't significantly alter guests' psychology, their desire to experience certain attractions over others, or their willingness to wait a certain duration for those attractions.
It's the same reason that today we routinely see 90-120 minute waits for things like Rise and Slinky vs a 5-10 minute wait for Star Tours. People don't view Star Tours as a suitable replacement for Rise, Slinky and a half-dozen others, despite the lower wait time. It's the same reason that Rock N Rollercoaster and Tower of Terror were 60-90 minute waits 8+ years ago, and today are still 60-90 minute waits despite the addition of Slinky, Rise, Falcon, Saucers, etc.
Would LMA reduce wait times at all other attractions? Yes, to some degree. But it wouldn't be as dramatic as you seem to imply. If the line for Rise tended to dip under 90 minutes during LMA, people would shift their habits in response. And as soon as those 5000 people are set loose, many will immediately move to fill the void.
Meanwhile, the addition of LMA would draw nominally more people into the park and raise the average length of stay. It's not the exact same population being drawn away from other attractions, and the draw itself would not be equally distributed. IMO a disproportionate number of guests attending LMA would be drawn away from other lower-tier experiences like Indy, BatB, Frozen, Launch Bay, Playhouse Disney, Muppetvision and Star Tours--experiences which themselves operate under max capacity.
As long as demand for the likes of Rise and Slinky remains high, guests will move to fill any void that is created.