I have done the same thing in the wire runs in my boat.
I suppose that if I got energetic I could use the existing RG6 cables
that are already run to pull a new RG6 and computer cable to each room
that we would want a hard connection for a computer. I'd have to move
the modem/router down to the utility room in the basement where all the
power and utilities come in the house from underground. It would still
be quite a project though. House has three floors above the basement and
some of those RG6 cable runs are pretty long.
Nah. Too much work. I'll stick to the wireless WiFi. It's working fine.