We regularly catch cheaters in our classes; I do so every term and report all the cases I see up to the dean. In my experience these have not resulted in catastrophic declines in teaching evaluations; the few unhappy with getting caught cheating are drowned out by the 80-90% who don’t cheat.
It is actually critically important that institutions take cheating seriously. Rampant, well-known cheating can tank the reputation of a program or institution, or at the very least serve to cheapen the value of the degree.