No, noone has discouraged me from going forward with my plans! I intend to run a dedicated circuit, as well as the CATV and FM antenna (also coax) to separate boxes located on either side of the stud behind the entertainment center.
To play it safe, I will drill separate holes in the floor plates from the basement up and into the attic, so that my coax and sheathed electrical cable are not 'squuezed' together through the same hole.
It can't be any worse than the current setup, in which the previous owner ran the CATV along the outside of the house in a 50' length of gutter and in through the gable vent.
Does anybody have any suggestions for snaking wire through an insulated wall? I may have limited access, as the wall separates the living space from the garage. I suppose I can cut some holes in the drywall on the garage site to help get the wires down the wall, then just patch the wall later.