If it is dropped, it very well could have mechanicals (duct, plumbing, electrical, etc) running through it. Is this in a basement? If there is attic space above it, you can get in the attic and take a look to see what is going on there. There are really to many unknowns for anyone to give you an idea of cost without more information.

If you have a return air, then I would suggest jumping up into the attic and observe what else is in there and if it appears it could be rerouted easily. In a perfect world, if nothing was running through there, the project itself is not a terribly large or difficult endeavor.

No one drops a ceiling for no reason. Bet it’s full of stuff. And it’s not an important room to worry over either. It’s a traffic path.

FLW used lower ceilings in select locations to create compression so that when you passed through into the higher ceilnged space, the release would intensify the feeling of spaciousness. Use that principle as well. Create a nice dark moody space out of it.

I doubt you can economically do anything about that ceiling, and I suspect it's that way for a reason. If there is ducting, electrical, and plumbing components directly above that, it could cost many thousands of dollars to redo, and that's not even considering that there may be load bearing structural elements to deal with. You could always consult with a contractor and possibly a structural engineer, but it doesn't seem worth the hassle. I suggest you just accept it as something to live with. Whatever money you put in to changing the ceiling would be a sunk cost that you would never recoup when it was time to sell.