Lots of half-baked conjecture.
Once again, LEP does not, in any way, limit the rate of growth. It acts solely as an absolute limit on growth. That's all. It has no impact on how quickly you can expand. And it will NEVER impact on how rapidly you expand unless it is completely reworked, in such a way that there was no reason to use approval for it in the first place.
The argument that having to divert lots of production away from research into wealth doesn't impact on research is ridiculous. It is essentially basing your argument on the idea that putting any production into research is unnecessary. If that is ever the case, then the mechanics which allow you to put nothing into research and still get lots of tech should be changed.
Your military argument is equally preposterous. The entire point of the mechanic is to force you to think about whether you can support and defend a new colony; to make mindlessly spamming colony ships into a sub-optimal strategy. It is about making the player make interesting choices, which Sid Meier once famously declared to be the entire point of a 4X. You have somehow managed to completely fail to understand that, and believe that making expansion always better is offering more choices than making a player genuinely think about whether he can support a new planet. It is also completely contradicted by your own stance on, well, everything else. The research penalty will force me to put more resources into research, reducing my ability to produce wealth and hurting my military. The productivity penalty from low approval not only directly reduces my cash output, but also reduces my ability to produce ships. According to your own logic, this means that using approval is worse than using maintenance. You are attempting to argue that using stacking maintenance is simultaneously too easy and too hard, which makes your entire position logically inconsistent.
The idea it doesn't effect culture is rubbish; aside from the fact that having to use more cash-generating structures directly reduces the primary source of culture (and, in fact, does far more than the tiny penalty from approval, since it attacks the base culture growth rather than only applying a % modifier), it also prevents you from just settling hundreds of unsupported planets and spamming cultural festivals.
And while you cannot prevent the wide empire from eventually developing its worlds to an equal standard as the tall empire, you can make that development slower and make the final result less effective. If the Wide empire must dedicate 50% of its planets to producing cash to pay it's maintenance, then it is not able to leverage its growth. This is achieved through the implementation of real, global negative effect, so that poorer worlds must be supported by larger worlds. Approval, as a local effect, cannot do this. This is why your own solution to LEP requires converting it into a global effect; because local effects do not work on a global scale by definition.
It's really not that hard. Approval, as a local effect which impacts on 1 build queue, is good for preventing too much power being concentrated on that one build queue. Wealth, as a global effect, is very good for preventing the proliferation of build queues. The two are not very effective at doing the other's job, without being massively reworked - at which point, they become less and less useful for doing their own. This is very, very basic game theory. It is not controversial. It has been done time and time again across dozens and dozens of games. I have not done anything particularly original by bringing it to GC3, and tbh the very idea that there's this much resistance to it is bizarre, particularly when the suggested improvements to approval-LEP require such enormous contortions to try and make it workable.
Finally, it really boils down to this: I've actually made the mod and played with both systems, and the maintenance-based system leads to a more interesting and challenging game - and not even by a small margin. Even before I implemented the AI changes, it was a better system. You have only played with an LEP system that you have outright stated should be completely redesigned from the ground up, and are simply attempting to hypothesize why a maintenance-based system wouldn't work; and most of the reasons you're coming out with are basically ridiculous. Your own proposal for replacing LEP is literally logically impossible, and you think that it's better than the present system, yet you cannot appear to grep the idea that a tried-and-proven method might be.