You don't have to write a "rhythmless' draft.
When I write, I write a scene, most scenes are 1000 to 2500 words (commercially there are typically about 250 words per page, so 4 to 10 pages, and my editor margins and typeface are set so it usually does work out to between 250 and 275 words per page).
During that writing, I edit, and edit, and edit. It's okay. In a way I write the whole scene at once, it can change in my mind. I may get a better idea, I may not like the way it sounds, I may feel like I am forcing a character to do something out of character, etc. I may feel like it is dragging, weighed down by too much dialogue, or too much description.
If I need to describe something in the setting, I'm going to beat my head against the wall until I get it right, dammit. I have spent a day on a few paragraphs describing a walk in a strange forest at dawn.
If a character has a way of speaking, I want it to "sound right" on the page.
I write the scene as best I can before I write the next scene.
That said, I am also ruthless, if I have to cut it tomorrow or a month from now or rewrite it, I will. (I keep daily dated backups, so hundreds of them, and if I wanted to go back and resurrect it for some reason I can.)
This happens, often because while writing, I will realize there are better finales or twists to be had, and if they need to be supported or foreshadowed or justified by changing earlier elements I will change them.
I am a discovery writer. (So is Stephen King and other famous authors). I don't plot a story beforehand.
What I have to start a story is just a compelling protagonist that I know well, and a problem they must solve. To stay alive, or keep their family alive, or save somebody they love, whatever. The hero feels compelled to solve the problem. If there is an antagonist, they feel the same, if the protagonist succeeds they fail.
That is it. Every character does the smartest thing they can think of doing, and as King says, the story will turn out somewhere.
Well, there is one more rule: No character can stall and just do nothing, not without losing even worse. No stalemates; a stalemate cannot be an acceptable outcome to either side. Then the story will turn out somewhere.
I encourage you to write as you write, but with the same determination your characters must have: There must be a stopping point, you cannot edit the same page or scene forever. Realize that at some point, rewrite is just making it different and not better.
I don't know what you personally consider "rhythm", but if you want it, figure it out, line by line, paragraph by paragraph. And don't rewrite until you are certain you are replacing it by something better. Do not rewrite unless you feel sure it is "better" and not just "different."
That may mean leaving something as it is "for now", because you have run out of ideas on how to improve the rhythm. So leave it, when you go back and read it, maybe you'll have a better idea. Maybe you won't.
Every line I write is the best version I have found so far. And that might be the final version.
Be your own writer. Everybody telling you how to write (including me) is telling you what works for them.
