I'll get to a nifty solution that meets one of your examples a bit better towards the end, but in the meantime....
There are likely several reasons (this hasn't been done very well until recently):
They would still require separate hardware to be projected on a separate screen bellow the main screen. While it may not be as big a deal now that we've gone all digital, in the days of 35mm the frame size was pretty much set, as was the hardware. For hearing impaired showings we had the ability to run a special DVD through a separate, standard office projector that would place the subtitles and "context sounds" on the screen for people hard of hearing, but we still had to set it up, angle it just right (not all theater screens are the same size/pitch/width), and then they had to be started at a specific time to be in-sync with the film, though some had hardware to help with that as well.
Further, placing them on a special screen has another downfall: tall patrons sitting in front of you. Not all theaters feature full stadium seating, especially for the first 7 to 10 rows in some larger screen theaters. Should you be unlucky and have to sit in one of those seats with a tall patron in front of you and you need the separate "subtitle screen", you're gonna have a bad time. The screen is optimally placed to try and reduce these problems as much as possible, but having one even lower would negate those efforts.
Special hardware like what you're talking about, glasses or stands that let people view the subtitles from just their seat while everyone else simply doesn't see them, still requires additional hardware. It's handy for the few hard of hearing/deaf individuals who come to the movies, but if equipment had to be supplied and stored to cover anyone and everyone who might want them, the cost would be insane. Which leads us to...
Cost. I remember when 3D first came to the theater I used to work for and relied on "shutter lens" glasses. They had to be cleaned and sanitized between showings, kids would drop and break them (we never charged for this unless it was clearly deliberate), and they cost something like $50 a pair. When it became possible to simply use cheap polarized glasses that the studios just sent in droves, we switched as soon as we could, even paying to have those screens updated to "shinier" ones to reflect light better and make the picture look less dim through them. Not everyone needs the film subtitled, so simply having special hardware for the few individuals who do is more cost effective and less prone to having some jerk who doesn't really need it breaking it.
A separate screen makes me have to completely take my eyes off the main screen just to read the text. Sit back far enough and some subtitles can be read peripherally. Placing them on a separate screen makes that even harder.
Basically, it used to be that we would have special screenings listed for hearing impaired patrons to come and see movies using our special projector. We also had special headphones we could link to each projector to provide hard of hearing patrons with louder, more focused sound. Now some theaters have special devices that can be placed in the cupholder of their seat, called CaptiView, so that only they can see the subtitles during any showing, making it more convenient for deaf patrons to see movies on their schedule.
Here's AMC's site on assistive devices for people with various auditory disabilities.
