J C Lawrence
1) Is it necessary to reinforce these cuts at all or am I just freaking out for no reason?
I don't believe there's reason to worry, though things were better when DTG laminated their boards (he is no longer able to obtain the lamination material he was using). I'd merely be gentle and not worry.
2) Regardless of 1), is there a way one can suggest to ensure that these will last for longer?
Treat them carefully. If you're really worried, and I wouldn't be, then using a single sheet adhesive lamination on the board front.
ObNote: My DTG games have been seeing play, multiple times per week, for well over a year now. None show any signs of wear.