I walked the route out-of-season, because summer is too hot for me in the Mediterranean. As a result, most of the resorts were closed, with barely a bar or restaurant functioning, let alone hotels. Mind you... I prefer resorts to be empty!
On the other hand, given the number of walkers I saw, I'm sure someone is missing an opportunity to 'sell' the route with a complete accommodation package. I know how these things work, from my occasional dealings with operators. If you try and book places yourself, then it costs you a few pence per call, and you might have to make up to five calls on occasion to get a bed for the night. With a package deal, someone else will do the phoning around, but rather than charge you a few pence for doing it, they basically charge you double for the accommodation, even if they've negotiated a discount with the provider, and basically that's their profit. I reckon that's fair enough, because I have come across people who are quite happy to pay over the odds to have all their arrangements made for them.
The other thing that's worth considering on Menorca is using a couple of bases on the island, then commuting to and from sections of the Cami de Cavalls using buses. You can easily find cheap digs in Mao and Ciutadella, close to the bus stations, and it would barely take an hour to reach most stretches of the Cami de Cavalls (plus maybe another hour to leave them and return to base). The only stretch where this won't work is along the rugged north coast. Buses don't serve the longest stretch, and there's no accommodation. Wild camping isn't allowed... but hey... do you think that stopped me?
Winter bus services are a bit skeletal in places, but it's easy enough to bail out by taxi. So long as you reach a road, you can call for a taxi using one number, and the taxi office will get the nearest available taxi to you in minutes. If you just use to taxi to get to the nearest operational bus service, then it won't cost more than €10. (Well, maybe €15 to bail out of a car park at the end of a dirt road on the north coast.)