Does physics education research support the idea that answer keys are bad?
I won't have a hard answer, especially one specific to physics. I did find some papers that looked somewhat relevant though. Please take this with a grain of salt as I've mostly just skimmed them, and this isn't my academic area of expertise.

This paper found that comparing different methods of reaching an answer was more effective than looking at methods of solution sequentially. This says more about how students might best use an answer key than whether they should get one.

This 1992 paper found that practice examining worked problems or completing partially worked problems was more effective at transferring knowledge than conventional problem solving. In keeping with the first paper, this paper by the same author showed that variability in the examined worked problems was also important. This would indicate that for a subject that students generally have a hard time wrapping their head around, like physics, the ability to study completed problems at the same time may be a useful tool. 

However this excellent article discusses how you can go too far the other way, with advanced learners fairing better without information they already know clogging up their study material. Overall this makes a mixed approach (some problems with worked answers for comparison, and some problems without available answers) seem best if the strength of the prior knowledge of students is unknown. (Assuming students gravitate to the type of material best for their individual needs.) 

(opinion on practicality) However I'd note that in the context of a college class, giving a set of completed problems, rather than additional turned-in assignments, doesn't create a pretesting point-of-accountability to further incentivise study. Also your department policy may relate to things like professors who sometimes want to reuse questions from previous tests. So attempting to change may be resisted because you may unintentionally be asking other professors to take on more unwanted workload.

Some of the research terms I found that you might want to look at further include 'Cognitive Load Theory', 'Aptitude-Treatment Interactions', 'Expertise Reversal Effect', and 'Instructional Science'. You'd probably also be well served by skimming through a proper textbook on education techniques if you can find one that's suitably well cited.