Set an example of what, MR. coloccw spreader of well-meaning misinformation?
I agree you should wait until after you get your F1 back to engrave your lower. That's good and reasonable advice, but that doesn't make getting the F1 back a legal requirement, nor does it make it wrong, or bad, or somehow un-American or rude or reckless to engrave it before you get your F1 back. Or hell, before you even fill out an F1 and send one in.
Use your head.