He looks like a human pint of Guinness! 😛
Personally, I think he looks ridiculous, and there are parts of Angel s5 where I am actually embarrassed for him! It's just so affected, doesn't feel a bit natural to me.
There are parts of Season 5 when I'm actually embarrassed for Angel, too, especially that "latest fashion" outfit from "The Girl In Question," and the whole puppet thing, but once Spike's "look" had been established, I suppose the bleached white hair and leather trench coat just became so recognized with the character that Joss was reluctant to change it. I know that at least part of the look, the bleached hair, was quite painful for James, and actually resulted in a scalp infection at one point.
The trench coat was Spike's trademark, and was shown in Season 7 to actually be essential to his own self image, at least "the old Spike, the Spike who almost killed me when we first met" needed it, and when Buffy made it clear that she needed that old Spike, the coat came back. I think that it is significant, however, that that original coat was replaced in Season 5. Granted, it was replaced by a near identical copy (with 10 spares hanging in the closet) but, despite the similarity to the old coat, it was new and improved, just like Spike, with his new and improved soul, was as well.
Those are the things that make Spike Spike, just like the battered fedora, leather jacket, and bullwhip made Indiana Jones who he was. Change any of that, and you change the character. Change the character, and you've LOST the character. That's exactly what happened to Angel and his crew in Season 5. They had developed their "look" over the previous seasons. Having Angel suddenly tuck in his shirt tail and wear a tie would have destroyed his image, just like cleaning Wes up would have destroyed his. The only major changes in "looks" in Season 5 (Gunn's and Fred's) resulted in a major change for the former and a total loss for the latter.
Both Angel and Spike had established their "look" well before that last season, and any major change presented the risk of losing a part of the character.
Now, if you really want to feel embarrassed by a character's wardrobe, there's always Lorne...