There is no valid reason why this should not already be a universal practice. If you are looking at any paper which cites the output of a custom-built computer program but omits the source code, it's probably safe to assume that the program is a mess and therefore the conclusions are not (yet) robust.
While it would be great and preferable to have both, isn't the code just a language/stack/programmer(s) specific interpretation of the underlying model?
There's the catch -- it should be, but there's no way to verify it's correct without comparing the source code against the model. (Well, I suppose if you had access to the raw data and the time to rewrite the software yourself from scratch, you could do that and see if you got the same results. But who has time for that?)
I'd definitely prefer to have both a model and an implementation available, but if I had to pick just one it would be the code.