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"if the hackers or botters have become indistinguishable from other competent players, then... Well, excellent! Mission Accomplished"

"... that a problem is absolutely subservient to the integrity and playability of the base game."

If you use hacks/cheats to help you play higher than your natural skill/ability, doesn't that ruin the integrity of the game? The mission is not accomplished in this case. Instead it's just tricky to determine who's hacking.

Headshotting everyone on-sight also sounds like the old days of hacks in games. In my experience, there is more nuance to the way these cheats are used these days. Most people aren't trying to be obvious about it.

Most cheats replicate things humans can do. They correct issues people have with their aim or reaction times.

Inhuman inputs are a thing of the past. Kids these days can do some pretty wild stuff at high levels of play.

It's not the impossibilities I'm worried about. Those are easy to see and report. It's the slight corrections which look "natural" but are actually the work of cheats "assisting" players.