You have way more practice spelling words than translating musical phrases from mind’s ear to fingerboard.
Also, for each letter, there is a fixed conceptual mapping of “letter in your mind” to position on the keyboard. For any word you recall how to spell, the sequence of letters is easy hold in your mind, so converting it to key presses is a fairly concrete task where you are identifying the next letter in the sequence and finding the position on the keyboard for that letter.
For musical ideas, most of us, even if we’ve memorized the note names on the fingerboard, can’t readily map an absolute pitch in our mind’s ear to a position on the fingerboard. For licks we know, we can probably relate the sound of the lick in our mind’s ear to the position-independent fingerboard shape of the lick, but I’d guess most people can’t hear a known lick in their mind’s ear and play it in the matching key on the first try.
If a person was improvising in their mind by “note name” rather than by “sound in their mind’s ear”, maybe it would be easier to translate to the fingerboard, but it’s not clear to me how a person would comprehend music that way on the fly. Translating a sound in your mind to humming is relatively straightforward (within your available humming range), but I find it difficult to believe anyone would be able to think a musical idea in terms of note names and translate it to humming as quickly.