The thing is, if the anticheat becomes any stronger, there is a risk for multiple false positives, especially if the anticheat isn't programmed to understand the state of the player (like if they have a speed perk, or if they have a jump boots.) I personally think just letting the surrounding players be the anticheat is a more resource friendly system to the busy staff team, but not the most effective one of course.
Because if the anticheat is given full control to make full judgement calls, false alarms may just end up being perm banned falsely, and if a user wasn't recording at the time, there may be no way to prove they weren't hacking effectively.
That being said, it's a more likely scenario that the anticheat may kick or tempban a user, but while mojang is trying to rid of all hacked client distribution, and we keep fighting, there will always end up being a way to bypass. An anticheat would probably need to take small parts of focus from the devs regularly, or at least one dev at any given week to pay attention to it to ensure everything maintains order, constantly tweaking parameters until a nearly perfect (because perfection is a near impossibility) system is made. But even then, if the system were to try to warn staff members to look at players, the staff members can also just be too busy to help carry out surveillance .
TL;DR: It's an idea that has great intentions, but this typically can't be as simple as installing an anticheat and calling it a day, I mean there are solutions to do so, and while they're somewhat effective, they aren't great with bypasses. I have my own ideas for a custom anticheat, but they're not surefire methods, and probably would be too resource ineffective to run properly.