Delmar, I've done that with a few things, but I'm a designer, and am easily bothered by small visual details. I'll know it's there, and yes, that's a wonderful first-world problem to have. For *embroidered* logos, though, agreed, it's the only way to go.
Ah, Nick, you've put your finger on the other and possibly best reason to remove them. 'This old thing? Oh, I picked that up at a yard sale." ;)