I don't know that we have anyone with expertise in this area, but I'll ask.
I've seen a bunch of films on Blu-ray discs, with beautiful high-resolution detail, even when projected on a moderately large television screen.
Then the discs have "special features", which as often as not look like some low-resolution crap the dog threw up.
Why do they do this? I can understand that some features (interviews with cast members, for example), might not have been shot with high-resolution equipment. But deleted scenes are presumably shot with the same equipment as the rest of the film - so why do they give us total rubbish?
One possibility that occurs to me is, maybe this is a disc capacity issue (higher resolution in the special features means you can have fewer of them). I guess that is possible, but it seems unlikely that this would be a big problem, when there is a two-hour film, entirely in high-resolution, sharing a disc with a few minutes of special features. I'm not sure what the capacity of a Blu-ray disc is, but I don't think I've come across a film yet that was long enough to require two discs (this does happen with DVDs). So if the disc can hold even long films in high-resolution, why can't it hold a shorter film and a bunch of high-resolution special features? (Perhaps I'm missing something here - the sub-possibility is that maybe there is a capacity constraint, and longer films are put onto Blu-ray discs with slightly lower resolution, to make them fit.)
Another possibility is, maybe it takes a lot of time and effort and money to take the footage in whatever form it is created in, and then convert it to the form needed for high resolution display on television screens. (Having converted some DVD material to a format which can be played on a tablet recently, I was shocked to discover that the conversion process takes longer than actually watching the material at normal speed, at least on my computer.) If it is less costly, less time-consuming, whatever, to prepare the material for low-resolution instead, maybe they only bother about the high-res for the main feature itself.
Or maybe there is some other explanation which has not occurred to me.