A lot of the federally approved vaccinators in my neck of the woods are employees of public health departments.
Do I think they give a rat’s hairy patootie about proper, and likely expensive, disposal protocols...?
Nope.
And not just public health departments. On a possibly related note...
https://www.epa.gov/newsreleases/gwu-hospital-dc-pay-108304-penalty-hazardous-waste-violations