The same tool used for drafting and for editing produces very different results, and the difference is not about quality of output. It concerns who holds the intent.
Drafting delegates the decisions
Asking for a first draft hands over what to include, what order to make the argument in, and what to emphasise.
The output arrives as a coherent whole, and coherent wholes are difficult to disagree with in detail, so it tends to be accepted structurally and edited only at the sentence level.
What results is a piece organised around the model's sense of how such a piece usually goes, which is the origin of the sameness readers detect.
Editing delegates only the execution
Supplying your own text with a request to tighten it leaves the argument, order and emphasis where you put them.
The model works on sentence construction, redundancy and clarity, which are the parts it handles most reliably and where errors are immediately visible to you.
Verification is also trivial in this mode, since you know what the passage was supposed to say and can see whether it still does.
The failure modes differ correspondingly
Drafting fails by producing confident content you did not verify, because you had no prior position to compare it against.
Editing fails by smoothing away the specific and the unusual, since the likeliest phrasing is by definition the least distinctive one.
The second failure is recoverable by reading the result, and the first is not, because nothing in the text indicates which parts were invented.
Blank page problems are real and solvable differently
The genuine case for drafting is getting started, and it can be served without handing over the structure.
Asking for questions the piece should answer, or objections a reader would raise, produces material to write from rather than material to edit.
This keeps the drafting where the intent is and uses the model for the part that is genuinely hard to do alone, which is seeing what you have left out.
Specific instructions beat general ones
A request to improve a passage returns a rewrite reflecting a general notion of good prose, which usually means longer and more hedged.
Naming the operation — cut this by a third, remove the qualifiers, split the long sentences, make the first line the claim — produces a change you asked for rather than a change you now have to evaluate.
Working this way also keeps the voice intact, because each instruction alters one property and leaves the rest of the text where it was.