The main solutions we have today are IP ban + VPN blocking using a database of known VPN subnets and adding them all to the firewall, and a similar fingerprinting technique which scans their folder structure of certain system folders.
Is latency going to be good enough on mobile data (especially if they're also using proxies) for a FPS, though? Sure, they're using cheating software, but I wouldn't be surprised if the software gets the information it needs to cheat too late often enough for it to be useful.
Sophisticated cheats in games like CSGO (and other competitive shooters) are usually very subtle, such as displaying enemies on the mini-map when they shouldn't be visible which provides a major advantage without requiring superhuman input, and the added latency is often negligible—especially when the info can be relayed to teammates and now you essentially have the entire team cheating with only 1 player suffering from a bit of increased latency.
And I wouldn't say this is an edge case either as in my experience the majority of cheaters I encountered are individuals that play on an alt account and offer a service to guarantee wins in ranked games.