Please correct me if I'm wrong about how to deploy MoCA

Xfinity’s coax cable comes in to a central closet in our new house. It connects to a splitter that feeds four critical rooms. At present, an Arris TG3482G Moca-capable router is in one of those rooms and that’s the only room with a wired connection along with the Arris's limited WiFi. (BTW, all I want is Internet -- no TV.)

Now it’s time to put an Ethernet connection in the other three rooms — for additional switches, WAPs, etc.

I always use UniFi gear, but I wonder if that would be too much trouble given the coax-only feeds to the four rooms.

I mean, based on my limited understanding of MoCA, with it enabled in the Arris all I will need is a MoCA adapter in the three other rooms. I end up with the 4-port plus WiFi Arris in one room, and an Ethernet jack in each of the other three rooms, where I can add switches, WAP's, etc. Sounds so simple!

If I want to use UniFi stuff and still employ the existing coax wiring, as I understand MoCA: I will first have to put the Arris and a DreamMachine in the closet where the splitter is (which means I’ll need to run power to that closet).  Then, I will have to put a MoCA adapter on each of the DM’s four ports — to convert to coax — and put another MoCA adapter at the other end of the coax, in each room.  So instead of buying three MoCA adapters, the cost will be eight MoCA adapters, a DreamMachine, and an electrician to add power to the closet -- all that to end up with an Ethernet port in each of the four critical rooms.  It seems nutty.

Am I misunderstanding or overlooking something?