If you do already have telephone and/or coax cabling in your home, it might be easier in the long run to just replace it to be honest. Ethernet sockets and cables are cheap, and don't consume power.
I was looking into MOCA, but eventually I decided against it due to pricing and latency concerns. In the end, I opened up the coax socket at my router, tied an ethernet cable to the coax cable, went to my office (room above the room where the router is), opened up the coax socket, pulled out the coax cable, and voila, I now had an ethernet cable in the duct.
It's not that simple everywhere, We have brick walls, replacing cables means lot of dust and repairing those opened walls... provided you don't damage anything already there.
So here I'm feeling adventurous for pushing 10 GbE over a run of Cat5E for the next decade or more.
True, although if you are lucky your cables run through cable ducts. My house was built in 1935 and has brick walls as well, but all cables run through plastic cable ducts embedded in the walls. Where I'm from this is very common, as virtually all housing has brick (or concrete) walls.
Unfortunately, I bet a lot of this kind of cable is stapled down along the run. And with enough twist and turns I'm not confident the existing wire wouldn't break while being pulled, even without the staples.
And you don't even have to lose the coax cabling. If you tie two ethernet cables to the coax cable, pull them both through the duct, you can then pull the coax cable back in place.
I was looking into MOCA, but eventually I decided against it due to pricing and latency concerns. In the end, I opened up the coax socket at my router, tied an ethernet cable to the coax cable, went to my office (room above the room where the router is), opened up the coax socket, pulled out the coax cable, and voila, I now had an ethernet cable in the duct.