Character is not a problem. Story is not a problem. Design? Meh there are better options.
You might have to go a bit deep for this one. Design seems vague. For start, do you mean design in attire? Kiryu has roughly more than 20+ outfits he can wear throughout the series including the spin-offs. A tuxedo, singer outfit, business man attire, actor attire, a doctor outfit, construction, scientist, and plus many other outfits that can also be out of the ordinary. He is like the Johnny Sins of that game. He literally played every role from what the series gave him. Well yeah people are not wrong, he was that talented.
Do you mean design in combat? well.. he literally has 4+
separate fighting styles depending on the game. They are all actually different where even if DOA somehow did include him, i'd still try to figure out on how they might balance him (or which fighting style they'll prioritize over). He actually has a lot to go over and I think TN might properly balance him and respect his entry, unless of course TN ruins the character which I doubt since they'd pay for his entry (as it should be). Diego is nowhere near that type of character and quality to how he was made, to which I also think he might be too good for this game. There are better options yeah, but there can be always better options regardless on what it is. If you had to "really" sink in, he's better than majority of the DOA cast due to story writing alone but it would be quite obvious that DOA peeps may get triggered by reading/hearing that which is good. I mean can't deny it, it's actually true lol.
In terms of his overall character and personality, Kiryu is actually a pretty interesting character with how one views things that actually makes sense to the real world (especially Y0). As the series progress, his life and the city he once knew started to change, which in turn forced him with the consequences and actions to what a city goes through including Yakuza politics and crime lords. It's the sheer moment and willpower to leave something to help people and to become the greater good. Anyways, this discussion is off topic. DOA is not on the level for that type of character if DOA itself doesn't grow up.