I am slow to respond to this thread as my daughter is a sub-titler and I did not want to contribute until I had her views.
She says she is fairly certain that the black box is there to ensure maximum readability, so the subtitles do not disappear into the background and become hard to make out. This is because although the subtitles without the box may be clear enough for someone with good vision, for people with eye conditions like cateracts and macular degeneration it's the subtle changes of colour that can be the first thing to go. A flat colour on black system is going to ensure accessibility for the maximum number of people.
Often when you see the plain white subtitles, they aren't actually plain white, there's a bit of scaling to black at the edges to make them stand out enough to be reasonably accessible to those with eye problems, but even then they can get difficult to read when the programme itself is actually light coloured.
She doesnt know much about the technical side but thinks that some of the systems in use are very limited in what they can send. With digital television, how the subtitles display is actually defined by your digital receiver - some boxes have a much more delicate size and font to the subtitle, so although you'll always get the subtitles displayed in the basic format the broadcaster chooses, if you check subtitles when you're buying, you should be able to choose a styling that is more pleasing to you.
Live subtitling (news, sport etc) is done through voice activated computers. Each live subtitler has to train the software to recognise their voice and pronunciations. Technically this is very sophisticated operation, but even then there are times when the human doing the work gets stuck. The first time my daughter went 'live' as a live subtitler she was rostered to do the local news from Belfast. She did fine with the presenter reading the news, they then cut to an interview with an Ulsterman with a particularly strong accent who spoke through his teeth without moving his mouth. She couldnt work out what he was saying and couldnt lipread to help herself. The item ended up not being subtitled. Remember subtitlers are human.