I think it is crucial to learn how to code with pen and paper. All computerization adds a mental burden, that shouldn't be there. Also this is a nice way to connect computer science with mathematics.
Even if it did, having to write down thoughts or code by hand at slow speed and without convenient way to modify it is significantly worse. Not to mention I'd constantly get distracted by my ugly handwriting.
If you prefer doing it the oldschool way that's fine, but don't force it on others assuming their brains work the same.
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.
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...