Almost everyday and everywhere, we heard someone praising a wife by saying: “她很体贴先生。” or "她是一个体贴先生的太太。" If it is wrong, why people kept on using 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.
I don't really think it is wrong.
Its translation should be: She cares about her husband very much.
Its translation should be: She is a wife who cares about her husband.
"体贴" is a verb, and it means "细心忖度别人的心情和处境，给予关切、照顾". For example, "体贴入微" "他很会体贴人". (quoted from "Modern Chinese Dictionary"). Sometimes it can be used as a adjective, like the examples in @Tang Ho 's answer.
体贴的 is an adjective for 'considerate'. There is nothing wrong with '体贴(的)先生' with 的 omitted
BTW, 体贴 is also a verb for "show consideration for". Using a verb or noun in an adjective role is a common practice in any language
For example, The Host of 品城記 has a nickname 吃雞小王子 (Chicken eating little prince)-- 吃雞(eat chicken) is a verb; the former tennis champion Steffi Graf was nicknamed "Miss Forehand" (正手小姐) by John McEnroe -- 正手 is a noun
体贴先生 standalone doesn't look right because it suggests that 体贴 is an adjective.
In the sentences “她很体贴先生。” or "她是一个体贴先生的太太。", 体贴 is used as a verb.
So, 体贴 can't be used as an adjective but a verb.
P. S. 体贴 looks like an adjective in 她很体贴. But体贴先生 itself looks more like a verbal phrase without a subject, which suggests an incomplete sentence.