(And this is if you're a jet flying at high altitude. If you're down where smaller aircraft fly, I can point to areas on the US west coast that don't have radar or radio coverage. Heck, there's parts of the mainland US that don't even have NEXRAD weather radar coverage.)
Is that a good comparison, though? It seems like NOAA funding for the NEXRAD sites is perpetually inadequate. The one in Portland occasionally has outages that last a while. I would have guessed that civilian air control radar is better funded than NEXRAD, and military radar probably so well funded that every square inch of CONUS is covered by at least one.
The limiting factor is geography. Radar coverage in the US is excellent, but the mountains out west make universal coverage hard, and there's some areas that just aren't cost effective to cover.
At 40,000 MSL, yes, everything in the US is covered. Below 10,000 MSL though, there are definite gaps - especially in the mountainous west. It's just physics, the mountains block the signal, and filling in all the gaps is cost prohibitive. Instead, they just tell aircraft to fly higher if they want radar service.
As for outages... ATC radar goes out all the time. You just never hear about it because they either switch to an adjacent, (slower) en-route radar site as part of CENRAP [2], or fall back to procedural control (voice position reports on the radio). Redundancy is baked into the system at many levels, both technical and human.
[1]: https://en.wikipedia.org/wiki/Joint_Surveillance_System
[2]: https://aviation.stackexchange.com/questions/9464/what-is-ce...
Most of the South Pacific / South Atlantic / Southern Ocean (Antarctic); a lot of the North Pacific / North Atlantic / Indian / Arctic outside of the major islands and direct routes has nearly no coverage.