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I can't think of an argument against it. As an undergrad I worked with a professor on some theoretical stuff that was published. It was written in Fortran. I'd love to go back and revisit that code. I don't think there was a single comment.
I'm sure it would accelerate research if this became the standard.
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Easy counter, the implementation shouldn't matter. By having multiple people write different programs to perform the same process you avoid perpetuating trivial mistakes that distort the results.
I'm personally for publishing the source because I'm favorable to FOSS, but having an independent implementation verify calculations is just as important as having an independent lab verify experiments.