Wouldn’t it work better if we added UVC bulbs under the shroud like hospitals do?

This is a great question!  Two part answer.  

First part is that it’s actually two different technologies.  Bulbs are usually used to clean items in a sealed container in a hospital.

Hospitals use UVGI to clean the air.  And it can be extremely effective.  Here’s respiratory virus transmission expert, Dr. Don Milton (MD, PhD) …” min 20 to max 1000 equivalent ACH. ”  Hospitals have excellent ventilation at 6 Air Changes Per Hour, so 20 ACH is phenomenal.  But, it’s an entirely different technology than bulbs.

2nd part, per David Elfstrom, IAQ expert, the bulbs will damage the filters and the air moves too fast.  Same basic response from Jim Rosenthal, also IAQ expert.