Without better software, science cannot progress.
Science can progress even without software - the only difference that software makes is rate of progress and its cost.
But the culture and institutions of science have not yet adjusted to this reality.
Did you ask yourself why ? Maybe, because what's now, just works for them ? I didn't see any description of problems on this page, that this manifesto wants to solve.
The code is the only definitive expression of the data-processing methods used: without the code, readers cannot fully consider, criticize, or improve upon the methods.
The code is not as important as descriptions of algorithms, and the ideas behind code - readers should not concentrate on the code, but on everything that's behind it, and if they want to verify results, they should write code themselves, in order to increase plausibility of the results by independent verification - including independence of code.
I'm not buying this.