I already explained why in a previous post, though the quotes were screwed up. I do wish this forum just defaulted to HTML rather than this horrible word interface. Anyway:
Global Morale = (global pop + LEP)/Global Morale
This was a central element in your proposed changes to LEP. There is a very, very basic logical error in this calculation.
And limiting military and colony expansion through maintenance isn't bad in any way, means shape or form.
Firstly, the game already does it - maintenance is charged on buildings as well as ships. Presently, maintenance is punishing 'Tall' empires, in that you pay more maintenance the more buildings you have - it's another of the many reasons I've outlined elsewhere why tall empires are punished in multiple ways while wide empires aren't punished at all, and is therefore another example of why using global stats to limit local problems and visa versa doesn't actually work very well.
Secondly, military size and number of colonies are both global measures, so the central problem of approval-based LEP doesn't apply - it's a false analogy.
Thirdly, your 'no sacrifices should be made' argument is completely inconsistent with the aim of slowing down expansion. The only way to incentivize a player to not always expand is to make it a sacrifice to do so - even if that sacrifice is an opportunity cost. And this is simply an opportunity cost, you can't build a ship AND have your 30th completely under-developed colony, you have to pick. Once you've developed a few of your core worlds as econ, THEN you can have both - comfortably (unlike the present maintenance system, where you can either have a new planet and a new ship OR build up the planet).
In short, this 'unacceptable military cost' line of your argument is simply absurd, and doesn't hold up even in the face of an improved AI that actually builds ships (which my mod also has). You are either wildly overestimating the impact that maintenance has (for most empires, it's actually lower for a well-developed planet), or have a deeply flawed understanding of basic game theory.
As to your other points:
1. The fact LEP doesn't do what it's supposed to do doesn't necessarily change the intent. The intent also doesn't mean it can actually do it, though. You want to change approval to a global stat in order to achieve it, which is downright convoluted even without the broken maths.
2. Merely because the effect of approval does the right thing does not mean that the mechanic of approval is perfectly suited. The mechanics of approval are set up to prevent individual planets getting too big, and so aren't remotely suited to it, which is why even those who support the effect think it's presently broken.
3. is basically irrelevant to the difference between maintenance and LEP, given it's only there to make up for LEP's failure.
4. I covered above.
and 4 number 2. Culture is entirely effected by economy when you actually need to devote increasing numbers of planets to cash. Every market center you have to build is a cultural center you now can't build. This directly impacts on passive cultural growth. If you have 15 planets, you're paying out 6 cash per colony (90 total) and can basically have 1 econ world. If you have 50 planets, you're paying out 13 gold per colony (650 total), and need nearly 7 times as many cash planets. Increasing the % of the empire which must be dedicated to cash directly reduces manufacturing, research, influence, hell, everything which you can use a building to produce. It is, once again, a matter of making the player pick between opportunities.
In short, most of the arguments you're putting forward are actually just a question of finding the right balance for the mechanic - unlikely LEP, which is a matter of the mechanic being unsuitable for the purpose it's being put to and therefore no amount of balance work will help, short of a complete redesign (which will, undoubtedly, ruin it's use for restricting 'tall' empires). A good feature for a mechanic for slowing growth is one where you will overcome it as the game progresses; the player gets a sense of achievement from overcoming each obstacle. A really bad feature for one is having to go back and re-assign land on all your existing planets to counter a stacking penalty; it adds lots of unfun micromanagement. Maintenance has the former, while approval has the latter.