Some states don't post certain heights, like if it is unposted in IL on like US30 it is 13-6 or above.
This. You might not even know if a bridge is under 16'0", depending on the state, because they don't bother posting above a different threshold.
Plenty of overpasses with a clearance of between 14 and 16 inches exist on interstate highways.
I'm not so sure that's true. 
It may not be true for inches, but it's definitely true for feet. Here are some examples just from my home state of Kansas
14'4" — I-35, South Haven
15'0" — I-135, Wichita
15'3" — I-70, Voda
The I-35 portion of the Kansas Turnpike has multiple 14'0" bridges. I'd show you some GSV examples, but the KTA doesn't label vertical clearances—meaning I'd be showing you a 14'0" bridge with no yellow plaque on the structure at all. Well, OK, why not? Here's one:
Bazaar Cattle Crossing, 14'0" in both directions.