Because ID does not support grayscale profiles.
Grayscale images are always put onto the black plate (as they should be) of the current document CMYK working space and are treated as being in that color profile. You can preview how they will print more accurately if you turn on OverPrint Preview.
If you want to be sure what you see in Photoshop is the same as what you will get in print from ID you can set up a custom color settings file using the Black ink from the CMYK profile as the grayscale space.
When I import them in Indesign they are darker than in photoshop and they also print darker.
Is your print destination a composite printer or an offset press?