Agreed. The faster you implement and correct the better it becomes. It's quite improbable that you'll catch a logical error in writing and not catch it while coding it up. It's also quite unlikely that a sketch of your plan will help you more than a debugger will.

I disagree, if you get into this habit, you risk missing the forest for the trees, which is much more dangerous : for instance that you should have used a different programming paradigm, a different programming language, a completely different approach at solving the problem than coding that, or even sometimes solving that problem might be an actual waste of effort, better spent elsewhere !

Design, tooling, relevance != implementation.

And not saying don't think just pointing out that careful handcrafted logic takes almost the same time to implement anyway.

Most problems are such that it's hard to know what really needs to be accounted for initially due to some janky interface or the language not behaving as you expected which can nuke the whole plan.

Writing stuff down can make you more confident about the approach and ironically lead to a dead end because you assumed everything was accounted for.

I can't tell if this is sarcasm or not, you have the word "pen" in your name!

Anyway, not sure if it's "guaranteed" to be worse than using a computer. Yes, you'll definitely get less help with pen and paper. But you'll probably end up understanding the problem better, without relying on GPT completion of code etc...