For me (Raspberry Pi OS, latest level) 1.6.1 actually introduced the problem! Specifically and only on Raspberry Pi Zero. It works fine on Pi 3B and Pi 4B.
I second @david1
Today I tried to install zerotier-one on a Raspberry Pi Zero and a Raspberry Pi 1 and both got stuck with this message during install:
Waiting for identity generation
I found some hint the issue might be that these models are using an older ARM6 architecture and building from the git repo is possible that I indeed verified and running a locally built 1.6.1 version of zerotier now on Raspberry Pi Zero and 1.