OP here. When we got back to our room last night, there was still no router. I don't know if the guy just didn't get back to our room or was waiting until after we checked out (this morning). I did see a crate on a dolly that had routers in it outside of one of the first floor rooms near us.
Some people do have direct front desk numbers at times because of problems during past visits. If they saved the number and called that number, they would actually be getting the front desk.
Don't know if that's the case here, but it can happen.
No indication on the brand/model of router from the "cart"?
There is a chance it is not for guest use (doubtfull but possible).
If it is for guest use, and it is done correctly, one or at the most two routers for each building unit would easily be enough. Commercial routers are way stronger than retail "junk" and would cover an OKW unit with ease. I set up an Aironet at Kidani on the 2nd floor 4 or 5 beads from the lobby and I had my signal in Johari (not at the pool though as I had hoped).