I'm pretty sure online games like that (e.g. Runescape) also check intervals between clicks, this one seems pretty constant. But Runescape can't detect clicking tools running themselves iirc, so they've got other means of detecting bots (random events)

While that is the case, you can get around this by using Mousekeys. I've actually set up a little machine to hit 5 on the numpad to click every few game ticks. From the game's perspective, I'm not cheating. But it is a hardware solution because a software one would be easily detected.

Also random events don't exist in Runescape 3, only Old School Runescape. The anti-bot technology implemented in RS3 doesn't seem to have been ported over to the older version of the game yet, perhaps due to it running on an older version of the game's engine.

Probably because bots ended up beating random events and they just use other, better tech now

Runescape runs in the browser so its anti cheat mechanisms are very limited I imagine. I'm pretty sure most MMOs (which run as installed applications) have more involved cheat detection going on.

These days Runescape (RS3 anyway) is an installed app rather than a browser plugin.