While I agree there's no need to wire every room of the house with cat5 and coax, I think it's premature to completely rule it out.
Starlink is slow compared to cable and cable is slower compared to fiber. So a starlink subscription might be a good backup, but not primary.
Consider wiring some cat6 or better just to be safe, in particular from wherever your main internet will come in, to areas on the far sides of the house and other floors, home theater, etc... where you can place mesh routers. Oh, and the garage too and the back yard/outdoor entertainment areas. Using Ethernet cables to hardwire these nodes together, a process called ethernet backhaul can significantly improve performance by providing a faster, more stable, and reliable connection.