Sure, if needed, because...why not?.
Probably lower resolution = less sharpness & higher noise level?
If you're packing a $10k tele prime or a 24-70L2 on a ff sensor, cropping might not deminish iq - but for the rest of us like /me with a 17-40L & 70-300L, the lens' sharpness is only so-so and severe cropping really shows as you cannot "downsize-sharpen" that much.
Well the question didn't involve the word "severe" in it nor it specified cropping to the point of ruining the image which of course is counterproductive and never needed. I guess I should've said, "if needed (and up to a point)...why not?".
This image was made with a 7D , which is not known for being noise free, and a 10-22 at 11mm... it was cropped about 20% because at the end I didn't like the right part of the composition as much as when I shot it...I had no problem printing it at 40x56'' and hanging it in the wall of a museum for an art biennale. There's plenty of margin before you effectively ruin an image if the image is good to begin with.