there is an organization called Software Carpentry that is basically like this.

however, the real problem has more to do with incentives and funding than it does knowledge of software best practices. right now, if you take the time to write thoroughly-tested clean good code, all you're doing is handicapping your research career against people who can churn out papers faster than you. you can see this because code from computer science departments is nearly as bad as in other fields, even from students who have had real industry jobs and learned how to do the right thing.

it does seem like in this case, though, because the scripts were actually intended as a tool to be used by others, the investment in more careful testing might have been warranted.

It's called an internship (for graduate students), but you're right that it should go the other way too but you'd run into a lot of money, IP, and institutional politics issues. Occasionally there are older industry people who work as staff scientists who get paid little and support the research effort in some capacity, usually IT. The biggest reasons why it doesn't happen as often are because in many cases, people who become professors have never done anything in industry, don't care unless funding is part of the conversation, or aren't motivated to have artifacts be reproducible. Their research group is a fiefdom over which they wield control, so unless they want to start a company on the side, they don't care about your programming skills and they don't like to give up any control.

A lot of the code used in research is hosted on Github and open for contributions. That would be an easy way to make an impact.

Uni Zürich also has a group that tries to connect non-academics with researchers. The focus goes both ways, but it could be something to look into if you're good with code and want to assist in some way.

Link: https://citizenscience.ch/en/

Why would the researchers bother with this? How does it help them?

Something like this is sorely needed because we are abstracting away layers of implementation details and quirks from the users of computational software. They are in fact abstracted away so much that a doubt that the author might have about the correctness of the software is almost never brought up in a research paper. It is just assumed that whoever wrote the software did their due diligence. You often don't see their code, and even if you do, it is incomplete or impossible to run because while the publication is designed to allow the reader to replicate the study, the same doesn't necessarily apply to the computational component that crunched the numbers to reach the conclusion of the paper.

Software Carpentry would be a good place to start: https://software-carpentry.org/

Do you know many developers with excellent mathematical and high performance computing skills willing to work for 30k a year?

I think this is the underlying reason that the way this connection happens in practice is via commercially available simulation software.