312.5MB/s is only for ProRes 444, which is a lossy compression scheme and you don't want to use that before post production (from Apple: "The R, G, and B channels are lightly compressed, with an emphasis on being perceptually indistinguishable from the original material."). For RAW multiply requirements by ~4x.
ProRes 4444 is lossy, but it's still more than enough for most projects. Drive was shot in ProRes 4444 and I deliver network television shows shot in 422HQ or 4444 all the time.
Raw is nice but definitely not strictly necessary.
Yes, though for someone as spoiled as me working on 5k/8k hyperlapses with D810/5Ds and getting absolutely gorgeous RAW footage where post-processing filters can do miracles, I vastly prefer shooting 4k RAW, which puts a lot of strain on technology, be it camera, storage and computer as well (nothing on the market is fast enough and no amount of storage is sufficient). The results when viewed on a UHD TV via 4:4:4 mode are phenomenal though. Of course, with 4:2:0 H.264/H.265 it doesn't make much difference and for scaling it down to FHD ProRes 4444 is sufficient anyway.