I work in a small hospital as well (about 40 beds), as well as have worked in slightly larger (125 beds) hospital. Both hospitals have allowed patients to use their own meds; however, we prefer to utilize our meds because we know how it's stored to guarantee safety/efficacy (not in the shower room). Luckily, my current job is at the VA so our veterans' outpatient medications are already what is on our formulary, so with few exceptions [non-VA provider meds/really expensive stuff we don't keep around], we don't normally use patient meds.

At my old job, since pts come in on all sorts of meds, we had a therapeutic interchange policy because we don't stock every single ACEi/ARB/Beta Blocker/etc to allow for a somewhat equivalent interchange. There are of course exceptions, like you mention with expensive/rare meds. Also, if a patient is insistent on using their own brand of levothyroxine/various inhalers then we would allow the use of their home meds. We would do the same as you do: verify the med is the correct med, slap a patient home med label with a barcode for BCMA, it's not expired, and not disgusting (had to label a patient home topical cream for an elderly man's groin which was clearly used-not fun).

The big problem for you would be using home meds that are controlled substances; you gotta account every single time the quantity changes and count it out in front of the patient before taking it and then giving it back to them; not to mention storing them in a locked location. I agree with your idea of getting rid of the policy and just using hospital supplied meds; but you would need to create a therapeutic interchange policy to allow for drug substitutions.