What is the benefit of parameterizing a jupyter notebook over just writing python that's not in a jupyter notebook? I like jupyter notebooks for rapid prototyping but once I want to dial some logic in, I switch to just writing a .py file.
It's a literate programming tool. If you find literate programming useful (such as Donald Knuth's Latex) then you can write a Jupyter notebook, add text, add latex, titles, paragraphs, explanations, stories and attach code too. Then, you can just run it. I know that this sounds pretty rare but this is mostly how I write code (not in Jupyter notebook, I use Markdown instead and write code in a combination of Obsidian…
Jupyter is a tool to do some exploratory interactive programming. Most notebooks I've seen in my life (probably thousands at this point) are worthless as complete programs. They are more akin to shell sessions, which, for the most part, I wouldn't care storing for later.
Of course, Jupyter notebooks aren't the same as shell sessions, and there's value in being able to re-run a notebook, but they are so bad at being programs, that there's a probably a number N in low two-digits, where if you expect to have to run a notebook more than N times, you are better off writing an actual program instead.