I'm from the northeast US. When describing the phenomenon of going to bed at night, or falling asleep, I always formulate the verb like that, as in "I went to bed at 10" or "I didn't fall asleep until midnight."
However I frequently hear the formulation "Last night, I slept at 10" or "I usually sleep at midnight". I'm interested in whether there's any interesting known dialect or historical distinction between the formulations. I now live on the west coast US and know many people who use these latter forms, and it still sounds wrong to my ear, like it's missing the helper verb (fall, go).
(The one case where I might crossover is in the sentence "I couldn't sleep until midnight", which sounds right to me, although "I didn't sleep until midnight" sounds wrong.)
It feels to me (though I don't have the professional vocabulary for this) that for me, "sleep" is an indefinite-duration, continuous action ("I'm sleeping"). So when I want to mark the time that it starts, I need to help it with "go to sleep". When I hear people say "I slept at 10", it sounds to me like they were asleep for only a moment, at 10 o clock, but not after, if that makes sense.
Best Answer
I don't live in America, but I don't usually say, "I fell asleep..."
Where I live, there seems to be a distinction.
"I slept at 10 o'clock" where I live seems to mean that we got into bed at ten o'clock.
However, we would then specify, "but I didn't fall asleep until eleven o'clock."
To my ears, there is nothing ungrammatical.
And, answering your other statement:
There is a slight difference in meaning to me: I couldn't sleep until midnight indicates an inability to sleep, whether or not you waanted to.
"I didn't sleep until midnight" could mean that you were unable to fall asleep as well, but it has an additional meaning of perhaps you just didn't, that is, you maybe sat up late reading a book, and so didn't sleep until midnight.