Quick disclaimer, I’ve been involved with FOSS shooters for something like 20 years now. I mention that to establish where I come from: in a FOSS game anybody can modify the game client all they want, so all the bullshit is out of the way from the start. You can’t hide behind make-believe notions such as “they can’t modify the client” – which is one of the major lies and fallacies of commercial close-source games. If there’s something you don’t want the client to know or do, you make it so on the server.
There is a lot of things that the server can do that can severely limit cheater shenanigans. If you don’t want them to see through walls then don’t tell them what’s behind walls. If you don’t want them to know what’s behind them then don’t tell them what’s outside their cone of view. If you don’t want them to teleport look where they were a moment ago and where they claim to be now and figure out if it should be possible. You get the idea.
Aimbots can be detected because at the core it’s a simple issue of the client’s aim snapping from one place to the target too fast. What’s “too fast” and the pattern of the movement can be up for debate but it can definitely be detected and analysed and reviewed in many ways – regular code, AI, and human replay.
If this kind of analysis is too much for your server to perform in real time (it was too much, 20 years ago) then you can store it and analyse it offline or replay it for human reviewers. You can fast-parse game data for telltale signs, analyse specific episodes in detail, and decide to ban players. Yes it happens after the game was ruined but at least it happens.
There are a couple of types of cheating that you can’t detect server side:
Modifications to the client HUD that help the player grok information faster and better. This is a large category that can include things like colorblindness overlays, font changes, UI changes, movement tracking on display etc. As far as I’m concerned that falls under HUD modding and should be welcome in any healthy game. Again, if you don’t want clients to have a piece of information don’t give it to them, and design your game in a way that such mods are mostly irrelevant.
Automating input. Again a large category that includes macros that speed up complex chains of operations. Can be slowed down by imposing server-side delays but you can hurt legit fast players this way too. Same as above, if this is what makes or breaks your shooter then perhaps you should rethink it.
Some of the most fun games I’ve seen did not care about HUD mods and macros and on the contrary embraced them. You want to write a macro that will auto-purchase the best gear based on your available coin after respawn? Knock yourself out, because what constitutes “best” gear changes depending of the circumstances, and a veteran with a pistol can smoke your ass anyway if you don’t know how to properly use that fancy plasma gun.
I’ve mentioned human review above which brings up an interesting feature that I don’t see implemented in enough games: saving and replaying game metadata. It’s stupidly simple to store everything that happened during a match on the server side and it doesn’t take much space. You can offer that recording to seasoned players to replay on their PC which allows them to see the match from any player’s point of view. An experienced veteran can notice all kinds of shenanigans this way – and it’s also an excellent e-sport and machinima feature that enables commentary, editing, tutorials and so on.
Edit: Oh, forgot one thing. You may be wondering, then why don’t the big game companies do all this? Simple, cost. Why should they pay for server juice and staff to review games properly when they can slap a rootkit on your computer and use your resources?