Nobody seems to mind much when artists imitate the style of ancient heiroglyphs and petroglyphs, for instance, even when they're imitated very poorly... are we just far enough removed from those ancestors, and their societies are dead enough, that we don't mind the imitation?

Hieroglyphs, no, not so much -- because modern Egyptians aren't so much with the worshipping those gods.

Petroglyphs? I know some very cool petroglyphs which, if rendered as tattoos, would be considered profoundly inappropriate and appropriative by the people who still think those are powerful signs and places.

I think a tat that looks like Juno would be awesome (though I think her right foreleg looks a bit off, there).