It's simply a legal thing isn't it? This is about gov-controlled signs. Billboards are private, so gov control over the contents of those would largely be illegal.
Yeah, you're probably right. On the other hand, billboards are regulated - there are limits on how big and distracting they're allowed to be at various levels. There's also precedent for federal regulation of highway advertising e.g: https://en.wikipedia.org/wiki/Highway_Beautification_Act (I do recognise this is different from state controlled signage).
I still think it's a bit inconsistent to have zero tolerance for additional cognitive load from official signage while giving billboards a lot of latitude. Probably the most reasonable argument is that official signage should be held to the highest possible safety standard because in theory drivers have to pay attention to those messages.
But I don't think the government's actions are evidence-based. It's possible that non-serious, sports or holiday messages have a positive effect on driver safety, i.e, the negative effects of distraction are offset by increased driver vigilance when important safety messages are displayed. I don't think it's been properly studied.