Why don't the agents do this?

I've viewed this as similar to a video game. Where AI where it is programmed to do what it's supposed to do (defeat the player(s)) to a degree. Until Neo showed up the humans were on the ropes. Neo forced the AI to go over it's limits as he pulled a role reversal on them. This he briefly and humorously remarks in the the sequel "hmm..upgrades"

https://www.youtube.com/watch?v=2vm2QcWVEqU

In other words the AI makes itself only as strong as it needs to be and only pulls out certain game/reality breaking tools when it needs too, or perhaps when it wants to. The agents in the clip assures themselves that Neo (a player) is just a human and an AI's programming is always superior and how it decides to defeat him is more than enough. Basically underestimating the player.

By the end of the movie and in the sequel, it doesn't matter though, the AI is no match for Neo, similar to a player mastering a game (the things you mentioned OP) or playing with an overpowered character vs. AI, whichever.

This is what I think makes Agent Smith interesting, he wants to break free of the AI because he knows it is limited and it won't note flaws fast enough or take advantage of game/matrix breaking things like Neo does.

I'm guessing it's connected to the physics of the Matrix. I know, I know, the people inside can - if trained and aware - alter the physics, but some rules must apply, and I think some of that has to do with the willpower of other people.

Take a fight with a Zionite like Neo: if Neo wills-up his strength to godlike levels and hits the Agent, the Agent has to absorb that impact. If the Agent takes that hit and doesn't move, maybe it's an unstoppable force meeting an immovable object scenario. In the classic sense, this is thought-experiment territory. Hilariously, might it cause the Matrix to "crash"? Boy, that'd be awesome... But, more likely, I think it would mean that instead of the energy partially dissipating as the Agent drops backwards, the energy would be entirely "absorbed" by the Agent's chest, face, or whatever. Not "absorbed" as in "shrugged off', but "absorbed" as in "Neo's fist is now coming out the other side of the Agent's chest with bits of heart pulp all over it".

Either way, IMDBrefugee down there makes an excellent point: this programme has rules. The machines don't break the rules. They defined those rules and then defined a "police force" to fight within the system. Only the humans have meditated themselves outside of the system (Morpheus talks to Neo about this in the training program).

The bottom line, as pointed out by IMDBrefugee, is that there are rules at play and the Agents aren't bending them or breaking them. The Agents are operating within the system. They have rules, they are just "better" rules than the other players. Neo and the others have "cheat codes".

Because Neo and Trinity had a gameshark and the agents didn't.