I don't believe the publishing model is significantly impeding progress in science , but that doesn't change the fact that the publishing companies are simply leeches, profiting off the work and labor of others. It's worth breaking that up, because there's no actual value there.
As a layperson who hasn't looked into this in detail, I can't tell whether or not the academic publishing racket has impeded sciences. But I do know it impedes public access to the findings of research that is frequently supported in whole or part with public money.
That public access to its own research is a good is clearly recognised (at least here in Australia) by universities, most of whose libraries are open to the public (as are the databases via in-library PCs, but not remotely). But you must be near one for this to be practically useful.
One example how it is messing up progress: Someone publishes a wrong study with loud claims. The press eager to report something new is racing to spread the false claims around.
There is no counter-balancing force - journalist have no interest in debunking the myriad falsehoods. But the public has a real interest in knowing, particularly when there are health concerns.
