As an astronomer, I hope this idea takes off. Unfortunately, judging by the reactions my colleagues have had when I've brought up this idea in the past, I don't think it's very likely.
Providing codes is imperative; they are part of the methods and should be available for examination to ensure the integrity of the science. Those conducting research funded with public monies should be required by the funding agencies to release the products of that research, not just the results, but the data and codes, too (absent truly compelling reasons, such as national security). Eventually, I expect funding agencies will indeed require this for astronomy, just as they do for some other sciences; journals could help the field along, could improve the transparency and reproducibility of research, by requiring code release upon publication.
Absent funding agencies and journals insisting on code release and the moral argument of reproducibility, what incentives would help convince code authors to release their software?
Impact Factor? -> Patrick Vandewalle, "Code Sharing Is Associated with Research Impact in Image Processing", CiSE 2012 http://doi.ieeecomputersociety.org/10.1109/MCSE.2012.63
It could also be the pressure of colleagues who, as anonymous reviewers, would always ask for the code whenever a paper depends on computation. Journal policies will not switch to REQUIRING the code anytime soon, but peer-review can add some pressure.
That's not the whole story and the fact that this article is getting published speaks to that, however I still don't think it's likely that things will change in the short term.
My friend Matt Turk wrote about a similar topic recently: http://arxiv.org/abs/1301.7064
Of course that should not preclude the possibility of replication as described here.
I find the idea of threats to job security misguided. In the particle physics world some significant code (not everything, granted) has been made available for some time; e.g. Monte-Carlo simulators like Geant or lattice gauge theory codes like those from MILC, SciDAC or FermiQCD. Even highly optimised code has been available. Users are requested to cite the authors. No careers have been harmed, as far as I can tell.
Also, the code itself is not much use for replicating results without making the data available too. This can be more problematic politically and technically, but even here there are good precedents in the particle physics world.
Which is good as a way of 'settling information' into a medium but an awful way for today. It's the equivalent of stone tablets compared to what's available today
It would be much better if the product of research could be shared in a more flexible format. For example, don't get me started on reading two columns PDFs in a computer screen.
Flexible formatting, attachable metadata, reusable "source code" (that could be an excel spreadsheet, a txt list of data, or source code per se), redrawable graphs, etc
We need a faster, more flexible, albeit official way of sharing data. Yes, there are ownership issues, IP issues, etc. But maybe having a more easily searchable/traceable system may help with this.
Metajournals are trying to do it, with an "Article" overlay to data/software publication : http://metajnl.com/. IPOL also tries to publish image processing software: http://www.ipol.im/. And there is also some work to interlink science assets (more than articles) on http://linkedscience.org/. \ I welcome publication models not based on "PDF standard" (ie an electronic clone of the centuries-old ink&paper text article), but simply sharing data/software is not sufficient. I think it is important to have an editorial line and a peer review, otherwise anything online would qualify as scientific communication.
Moreover, software and data is hardly sufficient by itself; it needs to be explained, documented, illustrated and discussed to be more than a "harddisk dump".