@Peter662@Susie5 A host is free to rent their space in whatever way they choose. They can book through airbnb, other platforms, their own website, personally, or a combination of the above. Airbnb does not own hosts.
What is a breach of airbnb policy is to have a guest contact a host through airbnb and the guest or host then tries to find a way to exchange personal information so as to circumvent airbnb.
I have had many airbnb guests who were wonderful people and who I would love to have stay with me again. I like it that guests can do their first booking through airbnb, as they are strangers to me and I to them. They and I then have support (hopefully) from airbnb should there be "issues", like not following house rules, leaving a pigsty behind them, etc.
But once I get to know someone, am fully confident that they are trustworthy, etc. and would like to host them again, I just tell them to email me if they ever want to come back. I know plenty of hosts do this.
There is nothing nothing nefarious or "a breach of policy" about this and not cause to report an airbnb host. As long as both parties realize they are on their own as far as working out any problems that may arise.