If the monogram's in a place where it'll only be seen by your housekeeper, so she knows which shirts belong to you, and which shirts belong to your son/brother/father, then fine. Get the monogram. Put it down low on the left shirt tail, or inside the collar, or someplace like that.
Otherwise, I agree with you that a monogram on a shirt is cheesy. Although I suppose it's less cheesy to wear your initials, than to wear a designer's initials.