Yup, no drip loop, either. My no-longer-used cable TV line has one, so I know exactly what you're talking about. The DirecTV guy just pretty much took the RG-6 cable and shoved it through a gap under my eaves, straight into my attic. I suppose I could grouse at them to come back out and fix it, or I could just fix it myself while I'm going through the trouble of doing the OTA antenna.
On the othe hand, if I call up DirecTV saying I had premium-mumble-professional installation and they installed something that's not up to code and created a fire hazard and blah blah blah, then I might be able to get them to deal with the proper grounding, upon which I could piggyback the grounding for my OTA antenna.