OP you might be onto something.
However, i'm reading the pocket as a flap, which would naturally droop downwards, but is held up by multiple snaps (for ease of access). If bombs are just held up by that flap, it would put a lot of weight on both armpit stitch and snaps, so both would tear near-immediately. Instead, i'm thinking of rubber bands keeping the loosely-pinned (you made a great point there) grenades inside while enabling their weight to be tied to his arms, using however many connection points necessary.
I started typing with the idea of a white zipper instead of a flap to hide possible bulging, and to hide opening by making it look like a stitch, but now i'm not so sure… With snaps if needed you could probably just slide anything sticking out between them to pull it apart… Does that mean Kaiji would have multiple coats, depending how much stealth is needed?
also, all of this weight basically demands a lot of core strength not to fuck up his spine long-term, and as for 'good at dodgeball'… We're both thinking of Rock Lee from Naruto, aren't we.
just realised i never posted my kajii coat design here. anyways here it is!
i tried to make it make sense, but honestly i think a more realistic explanation is that he just has a pocket dimension in his coat /j