That said, if its "just an aTV3", twice the price seems highly unlikely. I'll give you that.
But if it's not just a TV with an ATV3 (1080p, Siri, more apps) built-in, then what are you speculating that it will be that would justify a "twice the price of a regular TV" price?
p.s. the last thing you are asking for already exists -- as a non Apple-provided solution though. Works on all iOS devices, through web, and certainly there must be a OSX client too. Nifty indeed.
I'm curious what product you might be referring to. FWIW, here's my experience with this sort of tech: I had a TiVo for quite a long time, followed by a TiVo HD which used a cablecard. As the cablecard bashers here mention, there's a lot of stories of installers coming out and having "bad" cards, but I didn't experience any of that. And even with those who have, my understanding (and experience) is that once it's working, it never fails. Recently, I decided to give Windows Media Center another try (I had tried it for a while long ago) and bought a SiliconDust HDHomeRun Prime which is a little network-connected box with a cablecard slot in it. For about $200, you get 3 tuners with that. This, combined with XBox 360's in other rooms of my house, allows me to have all of the rooms share the central computer's recorded shows and for each XBox to play a different live TV channel, if desired.
Apple has plenty of talented software developers (and lots of cash to budget) to allocate a few folks to working on a Windows Media Center alternative, either to run within OS X on something like the Mac Mini or via a dedicated MPEG2-to-MP4 conversion chip, an even lighter-weight, cheaper device like the AirPort Extreme/TimeMachine.
Even with my present solution, I've experimented with a piece of software (I forget the name off-hand) which will watch your "Recorded TV" folder on the Windows machine and convert the shows to an AppleTV-compatible MP4 format. It will even automatically add the metadata to iTunes. This all requires too much hackery for the average person, though, so an all-in-one Apple-branded solution which handles all this heavy lifting would be great.
As I mentioned, Apple would be dumb not too have already allocated some of their software developers to this task years ago, but upper management may have held it off the market because of the difficulty in dealing with cable labs (?), but that seems to have loosened up now, as demonstrated by the recent devices by SiliconDust. On the hardware front, Apple could easily partner with SiliconDust or simply buy the company outright if they don't have a hardware solution in the pipeline already.
Again, though, I suspect that Apple has been putting most of their effort into trying to get the movie studios and TV networks to buy into their vision of a la carte or monthly pricing.