One big problem is actually pretty highlighted by my first thought reading #3 from the OP, the one about teleportation circles. It was "well, then anyone could do that."
And, really, this is a tremendous problem in the discussion that is just really hard to fix without specific abilities. Because anyone can input a code into a teleportation circle. Anyone can use special items or poisons to ground flying creatures. Anyone could deal a large amount of damage to a force construct (Ballista bolt?) The only one I'm not sure about is using skills to tear back open portals, but even then the same issue is there.
See, if I have a dead person, at a certain level a cleric can speak to that dead person. And at a certain, higher level, they can bring that dead person back to life, as long as the body is mostly intact. And at a certain even higher level, they don't care about the state of the body. If asked to bring back a pile organs as a person, a mid-level cleric has to say "that is impossible for me". Same thing with other abilities. At a certain level, scrying goes from impossible to possible. Creating clones of yourself goes from impossible to possible. Controlling the weather or reshaping the earth, impossible to possible.
But that doesn't happen for martials. In the current set-up it mostly CAN'T happen for martials. Martials can do about three things. They can use skills. They can make attacks. They can take damage. That's it.
Need to kill a powerful monster? That could be something for a martial, but also any Lord can spend the money to equip peasants with crossbows and Purple Worm Poison and now you have the ability to deal something like 50 damage per turn for three turns. It's expensive, maybe prohibitively so. But it also demonstrates that "deal a lot of damage" isn't impossible for low level fighters. There is no point where "kill this thing" or "do X amount of damage over time" goes from impossible to possible.
Skills? Sure, maybe you can make something like tearing back open a rift a DC 20 check... but that's imminently doable by a 6th level character with a +7 mod. They almost have a 50/50 shot at it. Even if you increase the DC to 25, they still COULD do it, it is just incredibly unlikely.
Taking damage is about the only thing that becomes actually impossible. Surviving a certain amount of damage is just impossible for lower level characters. But.... isn't that the most absolutely boring thing? Isn't "I can survive getting hit" usually just boring? After all, unless you can survive everything (effectively being invulnerable) if you can't respond to the damage effectively, you are just sandbagging until you eventually die.
And this becomes a big problem when trying to discuss high level martials, because there is never anything they are allowed to do, or even really discussed doing usually, that isn't just a bigger number on something they could do before. They don't get to break out and do something that was once actually impossible for them to do.