Why "体贴先生" is wrong? And why so many people use it?
体贴 can be a verb or an adjective. So which one is it in 体贴先生? It feels to be a verb so it's a verb + noun phrase. But no, the missing subject makes the phrase incomplete in meaning. Why is it not interpreted as an adjective? A 的 is missing in the middle.
Yes, 的 is not necessary in some cases, e.g. 漂亮小姐 is fine because 漂亮 can't be a verb. How the word is used mostly affects how people interpret, and unusual ones will be strange to native people.
In both of your example sentences 体贴 is used as a verb.