Short answer... No.
It's wrong for precisely the reason you mentioned. だ cannot be used with い adjectives, and verbs in たい form act as い adjectives.
だ and です are two forms of copula in Japanese. い adjectives do not need a copula to fit into a sentence.
As for why there's a discrepancy between だ and です with い adjectives, it's because です after an い adjective is not performing a grammatical role, such as the way it is after a noun. It is merely a way to put the sentence in a polite register. Making an い adjective polite without です is possible (it's the same transformation that gets us おはようございます from はやい), but using that form for everyday words rather than set expressions sounds ridiculously overblown.
As such, だ has no role to play after an い adjective. It is not needed for any grammar reason, and it's not needed to alter politeness.
I just noticed that in the last example you inserted an ん.
That's allowed, but it's because んだ is a colloquial contraction of のだ, and that の is functioning as a noun, and so だ is not directly following the い adjective there.
Thank you Leebo!
Also, is there any way to receive notifications when someone replies to me? It seems there isn't much configuration in Jisho.
Well, if you don't answer, so that means people don't receive any notifications about replies at all.
I don't think there is. This site is just run by a few people, and there isn't much traffic on the forums anyway.
I just happen to regularly check it in my rounds of looking for Japanese questions to answer.
Can I use だ with たい forms?
So for some reason in Japanese we can use です with い-Adjectives, but we can't use だ, which is supposedly to be the equivalent.
When searching for the inflections for the たい form (as seem in 食べたい、飲みたい…), I realized it works exaclty the same as an い-Adjective, but in Jisho it was stating that it was an Auxiliary Adjective, so I'm wondering...
I can or cannot use だ with たい forms?
It's correct to say "食べたいだ！" or "買いたいんだ！"？