If I actually paid the $100000 a month for cable (slight exageration), I would spring for the extra 5 bucks to get the DVR that records. The Apple TV is not a replacement for the cable box. Plus the cable box has way more channels that I will never watch compared to the few channels that Apple TV has that I never watch (because it requires a cable subscription that I refuse to pay).
/Rant
You are missing the point about cable companies charging extra for each set top box you have. Plus the UI on cable boxes suck consisted to Apple TV, Roku, fire tv etc.
With the Apple TV I have access to many channels/streaming services via native and airplay without the added fees.
I know someone who is using an antenna for OTA and an Apple TV, via her parents' cable subscription, to get all the other video streaming content she needs. This eliminates her from getting cable on her own.