Why not "Jeg har et viktig brev for deg." ?
Isn't it supposed to be et viktigT brev?
Adjectives ending in ‘-ig’ and ‘-isk’ in the masculine and feminine neuter don't add a ‘-t’ in the neuter singular.
May "I have an important letter to you" be considered correct?
Not in English.
Why not? The letter is addressed to you...
Indeed it is addressed to you, but the letter is for you.