Removing the signs would be theft of government property, and is punishable by up to one year in jail.

https://www.law.cornell.edu/uscode/text/18/641

Edit: I'm happy to hang out in an old pickup truck with a coffee and a shotgun and wait for someone to steal the signs. Just point me in the right direction and give me a number to call with the forestry service, national parks, or the bureau of land management when someone snags a sign.