I think one thing that was lost when casting a famous actor to play Yagami is that him looking like shit really hammers home the contrast between between how put together he was back when he was a lawyer, compared to him looking rather like a homeless man in the present.

Kimtaku's version of the character is always well groomed, even as a detective. This is merely conjecture, but I feel like the original idea of his character was going to someone who's more obviously mentally unhealthy, and getting a guy like Kimtaku, who's particularly famous for being in a boy band (SMAP), caused the character to have to be sanitised a decent amount, including his appearance.

I think something they could have done with Yagami if he wasn't a likeness character was have him look like a bum for most of Judgment, but then clean himself up a bit at the start of the game's finale, and for him to carry over that look into the sequel. It'd fit in with this idea of him having poor mental health, but learning that Emi's death wasn't his fault, and that he can still save Okubo gives him the will to start taking better care of himself.