Regarding how crazy it is to be a wrestler, yet not have a wrestling license. I'm pretty sure you're dealing with every state's individual athletic, boxing, or wrestling commissions for a license. Government bureaucracies are rarely efficient or easy. That was part of the main reason the WWF tried to move towards "sports entertainment" back when Vince took over, isn't it? Get away from pretending it's an actual sport, forget the work, and you can argue you can't be treated like boxers because you aren't actually competing in a sport.
I doubt TNA has a legal team to foresee or work on these things. Maybe some of the wrestlers forgot, maybe some of them were in the process of applying but got the run-around. Who knows.
There was a story in one of the dirtsheets a few years ago, they directly quoted some of the regulations from one state's athletic commissions rules for professional wrestling. Damn if they didn't make rules like they were either marks or desperate to be in on the work. It had rules ranging from limiting the number of minutes per match, prohibiting wrestlers from taking the match out into the audience and other silly things of the sort.
In the end, as independent contractors, it's the wrestlers' responsibility. Most promoters, with the exception of the WWE, probably expected the wrestlers to take care of their own working visas, travel documents, etc. But I could also easily believe there's some mark athletic commissioner out there that thinks he's doing his job by being difficult and not granting a license to some rassler.