Not a good idea. We don't need laws that punish people for indirectly hurting other peoples' fefe's, even if it is dishonorable.

Like you say, if there is some actual damage caused by lying about military service, that is probably already covered by some fraud statute.

And consider it from another viewpoint - I was once dabbling on a rightwingnut site where a retired navy guy was always whining about how he served his country and leftie scumbags didn't. He also spent a lot of time humblebragging about how he 'almost' got an appointment to the Naval Academy. I asked him a few questions about his experience, after which I began to gather hadn't involved any real risk (no combat service) and so, since he already disliked me immensely for being a cowardly Leftie, I asked him if he got paid. Of course he had, and was enjoying a military pension at a fairly young age, so I said, "Sounds like what you had was a pretty good job! How is that any different than a job in the private sector?" That made him really mad, so a tirade of insults followed, blah, blah, blah.

Finally I told him that I had been in the navy, too - I had accepted an appointment to the Naval Academy during the Vietnam era. But, it wasn't for me and besides that was the same year the war was ending, so I resigned. That really put his knickers in a bunch and he began yelling "STOLEN VALOR!! STOLEN VALOR!!!" For a month he trolled every post I made with that (apparently he thought I was lying...).

I am quite sure that if it hadn't been an anonymous blog, and if there had been a law about stolen valor, he would have sued me.

So, I'm agin any stolen valor laws.

You never change things by fighting the existing reality.
To change something, build a new model that makes the old model obsolete.
R. Buckminster Fuller