Question:- "Why there is 人 at the end of the sentence if it doesn't have any reason to be there?"
人 by itself, and 羞人 have two separate meanings.
人 = person, or people in general.
羞人 = is a compound word meaning being embarrassed, shameful, disgraceful.
Why have a 人 in 羞人?
Whether a person is embarrassed, shameful, disgraced, depends on the point of view, the judgement of other people, i.e. other 人.
羞, by itself already means embarrassed, shameful, disgraceful; however, with the addition of 人, it emphasizes the fact that "in the eyes / opinion of people", it is an embarrassing, shameful, disgraceful situation.
Also there is the question of compounds which are "inherently" a part of Chinese sentence structure. Every language has it's own inherent peculiar structure.
Therefore, consider the sentence 这个道服好羞 which is perfectly alright, grammatically, but 羞人, (besides the above semantic indication), is a compound that without which the sentence seems to be "hanging in midair" without a satisfying resolution, sententially.
Consider other compounds with 人:-
动人 = emotionally moving;
恼人 = annoying;
烦人 = boring;
All the 人 there are to show the fact that the "actions" in question have, in the general standard / opinion of common human interactions, the qualities that they depict.