> Actually adding special characters reduces the search space. Most places adding them also require them, which means for one of the 10 characters the search space is just those 5 special characters, and for another the space is just the 10 numbers, and there is still one more where the search space is just the 26 letters.

But you don't know which slot has the special character and which has the number, and that choice expands the search space again (agreed not mathematically the same as with no restrictions, but then again users don't necessarily explore the whole mathematically available space of passwords).