Yes, coaxial cable is absolutely required. Don't skimp. It has more bandwidth and it's 100% reliable.
When I renovated the basement, I bought a spool of quad-shield dual-line RG-6 cable with copper core and ran it to every wall in the basement and to every wall on the main floor. Then I ran a pair to every bedroom since I was able to use a riser to the attic. Then used a high-frequency splitter in the basement. This is how you get whole-house DVR working properly.
You *want* to have RG-6 copper-core cable to each point in addition to ethernet. You need it for all home television service. No matter cable, FiOS/fiber, U-verse, or IP-TV, they all use MoCa to communicate with the other TVs and you want to have that. Satellite also needs two cables to each point.
Plus your home DVR solution, whether cable, satellite, will use the RG-6 cable with MoCa to distribute the video to your TVs. The MoCa connection will be the only one that will allow you to reliably distribute non-buffered HDTV to all televisions in the house from a whole-house DVR. FiOS, for one, requires it.
RG-6 is not for analog--it's for modern televisions of all types.