In most cases, you know something is wrong once your typescript compilation takes more than a few seconds. At most, it could be an interesting DOS attack, but most continuous integration systems should have a limit on how much seconds they can run the compiler for. So it's really not a problem if you have constraints on resources...
So, if not turing complete, what kind of automata would you use to accept your language, say if you were designing your own language?
If the type checker takes too long, sonething isn't right.
At least if your type checker weren't Turing complete, you know it will finish at some point.
Seems like a non-opinionated classification of "overrated".
Or we could go even more meta, since no physical system is Turing complete due to the Bekenstein bound, so any expressible system is necessarily at most an FSA.
The problem is that you can't really tell when a long compile is an infinite or just a really long one. You want non-Turing completeness because your tools need to be reliable.