I've taken time to think about this and I both agree and disagree with you. I think you're right that my proposal would lead to one-trick ponies - I am definitely more in the 'stamina mechanic' camp on that one. I disagree that basic manoeuvres are traps, the effect I'm trying to avoid is players wanting to do things, but finding that they can't because they haven't bought or learnt a specific manoeuvre. Everyone should be able to try to knock someone over, or trip them up, or charge, and so on. Maybe not everyone knows whirlwind attack, or even how to feint for advantage, and yes, improvisation exists, but some things are so fundamental they should have fixed descriptions.
I can't see how you can approach a system that gives you lots of options without needing to reference things frequently (or know the rules). You either write them down on paper or keep a book open on the spells *ahem* manoeuvres page. Oh and surprisingly, I wasn't trying to be comprehensive with my first post.
The answer to these two parts of your rebuttal is fairly simple:
1) Create a unified and simple Stunt/Combat Trick resolution system that covers everything from trying to disarm an opponent to tipping a statue over onto his head. If there is a unified system, then the players and DM don't need to memorize numerous different sub-systems and corner cases in order to pull off cool tricks.
Furthermore, no list of combat tricks (trip, disarm, bull rush, etc.) will
ever be comprehensive. If you try to create a comprehensive list, someone will always come up with a stunt that you didn't anticipate. Therefore, a unified stunt system is the only way to cover every possible trick without going outside the rules.
This approach is fundamentally what pg. 42 in D&D 4th edition is. I believe other RPGs, such as Warhammer Fantasy Roleplaying 3rd Edition also attempt this approach.
2) Create a more simplified condition system. Instead of trying to make everything from from "dazed because a rock fell on your head" to "has sand in your eyes" separate conditions with individual effects, create a system that broadly groups conditions based on how much they generally impair an opponent.
For example, the videogame Xenoblade Chronicles has a pretty elegant condition track for these kinds of thing: Break (the enemy is slightly impaired/off-balance) -> Topple (enemy is knocked off their feet/ completely off-guard) -> Daze (the enemy is knocked senseless and otherwise unable to defend themselves). I believe condition tracks like these have also appeared in several D20 games as well.
3) Give special combat maneuvers to Fighters and other warrior classes that produce specific results better than standard stunts. This lets warrior classes shine better at weapon combat than classes that emphasize different abilities, and keeps the stunt/trick system simple.
Why should you be encouraged to use different things in a fight? If something works, you should use it. I agree that spamming is bad and think a limit on how many things you can do in a single fight is a good idea, I just don't think they should all be different things (ie: I don't like encounter powers for martial characters).
It is important to design the rules to encourage players to mix up different maneuvers simply as a means to keep combat dynamic and interesting. Every fight scene in movies, books, and games has always benefited from being more dynamic. Forcing players to weigh the opportunity costs of using their powers also makes combat more tactically interesting. I won't say that 4E style encounter powers is the only way or even the best way to do this, but some sort of mechanic should encourage this.
Point 2 is bizarre because any increase in options will require notation in front of you or referencing. Do you memorise your 4th edition powers?
It is the difference between having to look in only one book to read the complete maneuver, and having to cross-reference feats from three or four different books to know the exact effects of your charge. Any feat-based system has a risk of ending up like 3rd edition, where I had to bring the PHB, the PHB 2, and a Complete book or two to every game just to cross-reference feats.
Point 3 I can sort of agree with, though I'm not someone who thinks they should be throwing mountains (as the current adage goes).
In BECMI D&D, a Fighter could throw a bola around an opponent's neck, causing the opponent to strangle to death (a save or die). I think that kind of stuff sets the bar for what should be possible in a D&D combat system. If the wizard should be able to cause save-or-lose effects, the fighter should have them too. It doesn't have to be ridiculous, but it needs to match a wizard's fireball or disintegration ray in power.
Point 4, well, yes, but not for the sake of it, design them with genuine thought about how combat works: rather than Cascading Catapult Slam (ridiculous name, ridiculous power) you have a simple attack and push someone and if they hit someone else maybe they are both disadvantaged for a turn.
Heh, you haven't watched enough anime or played enough videogames if you think Cascading Catapult Slam is a silly name.

I have seen way funnier names (Japanese Kanji attack names don't translate very well into English).
Anyways, I am huge fan of stuff like Greek Myth, the Four Classical Novels of Chinese literature, myth and folktales in general, plus anime and videogames. So, my preferences lean towards the over-the-top and crazy. Characters from myth can and did pick up and throw mountains around. I sorta hope epic level D&D characters could do the same.
Still, even if you do limit combat to something more down to earth, the possible options should still be far more powerful and cool than just attack, disarm, and trip.
That's nice and all, but quantifying this adds little to the discussion. As I pointed out, there are more reasons to gain advantage than just dealing damage - damage is not the endpoint of all D&D abilities.
No, damage isn't the end-all-be-all, but any option needs to compare favorably to just doing damage. As is, granting advantage with an action isn't worth it if you are the only character to benefit from it. If other party members do, it might be beneficial, but that is dependent on a lot of other factors. In any case, it is important to avoid stuff like certain 3E or Pathfinder feats that give options that are
always strictly worse than making basic attacks. Any system that doesn't hold up under mathematical analysis is worthless. Just because something sounds like it might be helpful doesn't mean that it is.
In any case, the endpoint of any D&D combat ability isn't damage anyways, it is bringing a fight to a end without lose on the party's side. As such, there that are many things that are more valuable to that end than others. For example, in the current 5E, something that knocks an enemy prone is fairly useless, since an enemy only needs 5 feet of movement to get back up. Since knocking an enemy prone doesn't prevent their movement, it doesn't have the defensive considerations it does in other editions. Immobilization is far better in that regard.