@Hugo550 Many hosts list on multiple platforms, rent through their own private website, etc. There is nothing "against the TOS" about this.
What is against the TOS is having a guest contact you through the Airbnb platform, and then surreptitiously directing them to a way to contact you directly, thereby circumventing paying the Airbnb fees. And I wouldn't trust a guest who asked me to do that, either.
Most hosts would never agree to this anyway, because we don't want to have some random stranger in our homes we know nothing about, with no possible support from Airbnb, nor do we want to do something unethical.
In my case, as a home-share host, I have quite a bit of interaction with my guests- it usually ends up feeling like I have a friend staying, or a long lost relative. If they've been here for a week, I have a pretty good sense of what kind of person they are. So if the day before the booking comes to an end, a guest were to say "You know, I'm really enjoying my time here and there's nothing I have to rush home for, so if you aren't already booked, I'd love to stay another couple days", I would have no qualms about them just paying me cash. Not particularly to avoid Airbnb fees, but because it's so much less hassle than having to spend time on the site extending the booking, encountering frustrating tech glitches, etc. And when guests finish an Airbnb stay and are ready to check out, I always tell them they can just contact me directly if they ever want to come back.
It's like if you met your wife or husband through a mutual friend who introduced you by inviting you both over for dinner. Once that event is over, you don't have to invite that friend to have dinner with you and your new partner forevermore to show how much you appreciate the facilitation of your first meeting.
If I had an entire house listing, where guests did self-check-in, and I never really got to know them, I would likely not so easily be willing to book off- platform, because I really wouldn't know if I went outside the platform, if they might take advantage of that by leaving the place a mess, or sneaking in more people, or not paying me after I've held the space for them. And they wouldn't have a bad review to worry about.