Could you give us some recent examples? I'm always on the lookout for new things to try that will make my DM wince as she tries to adjudicate them.
Examples from actual play:
1. Tearing a tapestry off of a wall and throwing it over a medusa's head, then grappling her to eliminate her gaze attack. (successful)
2. When characters who tethered together already becuase they were on a slippery sloped corridor were attacked my character (a Goblin) ran under a large monster with the rope, then tripped him. (successful)
3. Kender Misty jumped on to a dragonnel that was trying to escape (partially successful, the Dragonnel did ot escape, but I plummeted and went unconscious when he died)
4. Running up the back of horses pulling a wagon and leaping through the air to grab on to a flying Cambion who was trying to steal a shield we had (unsuccessful)
5. Using Intimidate to call on enemies to surrender (used many times, successful sometimes, unsuccessful sometimes).
6. Using the help action so a Sprite familiar shooting arrows tipped with purple worm poison (in addition to her own poision) would have advantage on the attack. (successful)
7. Grappling enemies then moving them up to be attacked by allies who did not want to get hit, then moving them away. (successful)
8. Disarming an enemy of his legendary elemental weapon and then throwing it into a portal to close it. (successful)
9. Grappling two enemies then dodging on sucessive turns, giving them pretty cpermanent disadvantage on all their attacks. (done many times, usually sucessful).
Any player with good abilities can try these things, but the opportunity cost for doing them with a spell caster is generally very high. Figters and Rogues are ideal for these sorts of things do to the ability to have a high Strength and Dexterity without having to worry about a casting stat. IME you can also run a 10 or 12 Constitution on a fighter and invest in Charisma too, but I know most here will disagree with that, and not running a high constitution does necessitate a certain play style.
What made you feel that? To me, the 4e fighter powers fit the "master of tactical and martial combat" fantasy extremely well.
I hated three things about this:
First that not all classes could do them. You are talking about fighting with weapons, I get that people that train should be a little better, but not that much better.
Second it doesn't make much sense. I can take a rifle out to the range tomorrow and shoot all day long and it is not like I can say - Oh I am going to use my once a day expert shot now. I will be shooting pretty much the same at the end as at the begining
Third supernatural things like lightning bolt were about the same damage as their equivalent fighter powers. It shouldn't be, it should be a lot more.
I know people on this forum like 4E design, but I don't think that is a commonly held opinion.
Why without using their powers or spells? Surely powers and spells are an inherent part of a class and so should be taken into account when comparing performance.
Because the fighter can do it without using powers or spells. Spells are absolutly a part of performance and that is WHY casters SHOULD be more powerful than classes without spells.
If you don't like this then just give the fighter spells so they can keep up. That would be better than letting them just flat outclass every other class.
For example the bladesinger's power that lets it cast a cantrip spell alongside an attack is what lets it keep close or exceed fighter extra attack damage, but is also more thematic for the bladesinger than just giving them the same extra attack progression of the fighter.
They can't generally exceed the fighter's damage considering the larger number of attacks, fighting style and the extra ASI in the class. They can keep it close, especially if the fighter is not optimized for damage.
I am fine with the bladesinger, my point is I want to keep it close and if you make a mechanic that adds another 20 or so DPR to a fighter they won't be.