I am a scientist and I have been a postdoc (and government grant manager and industrial scientist). This is not new, but is more new to biology than it is to other fields.
This problem is real. Our best researchers can't find a job and are "sitting on the sidelines." The investment in those folks by the government (i.e. your taxes) is going down the drain the longer they're unable to do meaningful work.
My feeling is that the underlying problem is the insulation of academics from the commercial world. Most science professors don't know what is involved in commercial work, don't know the relevant skills for commercial work, and don't have a network for landing jobs for students in industry. There are far too many professors who don't know how to train their students for anything other than academic work, and some who are adamantly against training their students for jobs outside of academia.
The result is that industry jobs that many PhDs expect to get go instead to people who left school with a BS or MS and received more relevant on-the-job training in industry. The truth is that there are very few jobs where the experience of a modern PhD is more meaningful than 6 years of industrial bench work. The government and academia still hire preferentially by degree, but those folks can't hire enough people to put a dent in the supply.
To fix this problem we need radical changes to the way we pursue science. Some possibilities for the future:
1) getting a PhD is "for fun." This is the current reality. If we all accept and understand this, that PhDs have no competitive advantage over MS students in the marketplace, there is no problem. If we do nothing, this will continue and will eventually make the PhD system obsolete.
2) Control of research direction shifts toward industry (i.e. professors become subcontractors on grants to people like Merk and IBM). I doubt many academics would like this, and there would absolutely be problems, but it would generate students with broader skillsets and networks.
3) Control of research shifts back toward government labs. This used to be the way things were. Government labs sat between industry and academia and facilitated movement of people, ideas and funding. Entire funding agencies that supported these labs are gone. Grant managers and review committees used to mostly be active scientists at government labs, that's no longer the case. This would be expensive to get back to and would really be unfair to the foreign scientists making up the majority of our young scientific workforce.
4) Set everyone on the GSA scale. Right now you can get a recent grad in his 3nd year of work funded at $60k/year on a grant to a commercial grantee, but it's almost impossible to get more than $25k for that same work done by a "graduate researcher" in academia. (Even if professors want to do right by their employees, they often can't.) So, don't allow any more $20k/year graduate students on grants. Everyone gets paid based on a combination of local cost of living and experience (years & degrees). That's the GSA scale (ok, it kind-of is). Removing the discount for students would remove free grad school for scientists, but would immediately fix the problem that the best bench scientists can't find jobs.
Whatever happens, the solution is not going to come from inside science. Scientific leaders range from completely disgusted with the human trafficking which is the modern research economy to openly hostile to the idea that this problem needs to be solved. Most people just don't know what to think. There will be no consensus amongst us in science on what, if anything, needs to be done.