^I think you're conflating sensor quality with codec quality. To make a long story short, if everything you said about raw is true then photographers wouldn't bother with raw either.
And as far as the advantages of downscaling go, look at the footage coming off the BMC that's been properly graded. It's easily as good as the c300 (8MP vs. 2.5MP). And the downscaling helps reduce some artifacts, but it doesn't make it sharper necessarily.
Yes. It does. The nyquist sampling theorem states that if a system samples at a given frequency then it can record half that frequency accurately without aliasing. So a 4k sensor array can resolve a perfect 2k image without aliasing. But most people don't care about a little aliasing, which is why, as you point out, the BMCC can resolve 1080p nearly as well as the C300. A bayer chip can resolve 70% or more of its stated resolution if you don't mind aliasing. The BMCC is reported to exhibit pretty bad aliasing. (Even the Alexa, a 2.5k array, has a bit of aliasing, but it's really minor.)
When you work in photoshop, you're not working in RAW. Your end product, even if it's a TIFF that's going to print, isn't RAW. The advantage of a RAW workflow is flexibility at the cost of speed. Not so much image quality. The data will be processed and turned into RGB (or whatever your colorspace) pixels eventually. But in theory, RAW will always be the most flexible format. I think we can agree on that. Flexible does not mean best. If I sacrifice a tiny bit of flexibility with the Alexa by shooting prores instead of arriraw, I get insignificantly less resolution, a codec that actually edits in real time, and the same latitude as I had before. A competent shooter handing footage to a competent post house will produce the exact same image on that camera whether using prores or RAW (totally impossible to differentiate) assuming the exhibition medium is tv. For theatrical 4k projection, RAW will offer a very small amount more resolution (but not a lot, Arri has just added 2k prores video so theatrical shooters don't have to bother with what a pain in the ass arriraw is). Only the most inept shooter, totally bungling white balance and exposure, will notice any significant difference. Or the most brilliant shooter--Deakins claimed he noticed a slight, nearly imperceptible resolution edge when screening Skyfall tests shot on arriraw and upscaled for IMAX, though no difference in DR as compared with prores. Fwiw, it all looked much better than Red's 5k, used on some additional photography. The bigger difference is that prores files will be vastly faster to process. High end video doesn't look like a compressed JPEG (which is designed for delivery, not as an intermediate format); it's very flat and much less compressed. Some day when computers are way faster there may be an advantage to RAW video that outweighs the disadvantage in speed that comes from working with it, but how much Alexa footage is shot in arriraw vs prores? Very, very little. Game of Thrones looks fine to me. In Time looked fine and that was recorded in uncompressed HD video, not arriraw. Red forces you to use RAW but most producers wish it didn't.
Furthermore, it's not JUST sensor quality. The Alexa has a fine sensor, but it's the video processing (colors that emulate 5219 stock extremely accurately, high and low gain path merging, how the prores codec is implemented) that matter. And a poor RAW developer (just look at how many permutations redcine has been through to arrive at its current implementation, which produces rather boring colors) can be problematic; not everything is as good as Adobe's plug in, which is slow. Arri's in-camera software is better than any results you can get out of red's RAW developer. You need a Pablo or Da Vinci system to get a decent look out of that camera, and even then it's not ideal.
Have you used any of these cameras or are you just reading specs online? Granted the one camera you mention that I haven't used (the BMCC) does seem to have the best IQ for the money by far. So if that's your only concern, go ahead and buy one. Canon isn't catering to the testbed-in-a-box Frankenstein's camera market (not necessarily a bad thing, just a pain in the ass for both shooters and in post). Black Magic and Red have that covered.