What don't they instead work from the opposite direction:
Create an abstract model of a Collatz loop that doesn't end with 1(instead looping back to same number) and prove it can't exist(Reductio ad absurdum).
[1] See https://en.wikipedia.org/wiki/Collatz_conjecture#Cycle_lengt... for a few references. The most recent appears to be the paper "Theoretical and computational bounds for m-cycles of the 3n + 1 problem" by Simons and de Weger.