A little historical follow up
The Liber Pontificalis says quite explicitly that Peter ordained three bishops: Linus, Cletus, and Clement. The presumption is that they served concurrently, not consecutively.
https://archive.org/stream/bookofpopesliber00loom#page/4/mode/2up
Seems to jive with Hermas, no? And possibly Clement’s “we”? (Linus and Cletus are thought to have been dead already when 1 Clement was penned).