They do, though they don't use it anymore. They believed they were doing the greater good by preserving the "Sacred Timeline" as dictated by the Time Keepers. It was all a lie, though. Fortunately enough of them say sense after everything came to light.

[Even though for a brief moment Loki had thought to make it easier and continue pruning.]

I am no longer at the TVA. Or I wasn't just before Thirteen brought me here.