Not bad at all. Has that old timey rustic feel to it.
So, if I have this right, there are three different basic styles of cabinets: Frame-less, which is what you have done has no frame around the box, hinges are hidden on the inside, and the door panels cover the box edges; Face Frame or Inset, where the doors sit inset into a perimeter frame that covers the front edges of the box; and Raised Panel, where the doors overlap (sit proud from) the face frames, but do not cover them. (I'm going from memory here, and despite recent suggestions to the contrary, I am not an expert finish carpenter, so this might not be the exact terminology, but you get the idea.)
If your door is wide enough, you could add a little strip of solid wood to the hinge and latch side, like a face frame, cut the door slightly on each side to inset it, and then screw the hinges and latch to those.
Aside from the risk of bending a hinge plate, or the hasp, I kind of like it the way you made it. It's got that old time purposeful look to it. Old is new again.