I don't think that looks bad at all. I've been grilling traditionally-formed doughs and grilling them, and I'm finding the edge crust doesn't really char up to my preference.
Usually, I just make a simple flatbread, with no raised edge, grill it quickly one side, flip it, top it, then let it ago a very, very short time to finish.
The crust will be extremely thin, like a cracker (but not flaky). It's not my favorite style, but we'll do them when guests come by and set out a variety toppings, like a pizza bar.