Indeed, even beyond tealite stoves, I'll pick a fight and say it pretty much applies to all alcohol stoves. They're best at boiling water. That's about it.

Yes there are some alcohol stove models that can "cook" and simmer better, but for me they start getting awful fiddly, and the nice simplicity of just using them to get boiling water goes away. If I need to "cook" more than boiling water I switch to a canister or white gas stove.