Here is the first plausible hypothesis I saw as to why waves end (there is no kind of herd immunity anywhere).
In short, the idea is that average R is driven by a few super spreaders, say, 10%. However, as the wave progresses, the growth of regular cases outpaces the super spreaders, diluting them from 10% to 5%, which in turn reduces the entire R below 1.
It is possible Delta is more concentrated in fewer superspreaders, hence waves peak earlier.
One explanation why there are more superspreaders in the beginning is because it starts by people who have many contacts and go out a lot, who constitute a large portion of the total cases, but eventually it hits people who are staying at home, lowering the average rate of contacts and transmission.
@biobook would love your opinion if I understood these threads correctly.
https://twitter.com/whiterabbitwb/status/1425670091941634051