We have rented our summer house for decades. Often to the same people each year. They were acquired by renting through a real estate agent or work-related posting. We simply provided a direct way to contact us, if they were happy with their stay and if we were happy with them, we'd offer next year same deal but direct booking.
We also made it possible for successful renters to refer and if that referral works out, we give them a non-financial gift, a welcome basket or vacation related activities. Air BNB is really good at one off renters, but really those are not too interesting term, lots of clean up.
It not just an issue of having more control or avoiding host fees. Airbnb and VRBO weren't able to give me maximum occupancy. I threat them as channels and that works well for me.
God forbid you ever have to use airbnb for an insurance claim you will really then see how hard it is to find anyone at Airbnb. We have been dealing with a claim for over a month and still cant even get to speak to someone that is an actual claim adjuster or anyone besides there "Virtual Ambassador".
AirCover for Hosts is not "insurance" so you won't find a claim adjustor. You just need to keep phoning until you find a customer service agent who can help you.
Why on earth would you have to advertise globally?? I've got three properties up and running for 2 and 1/2 years and I've only had.... Maybe two international guests.