Surgeons need to walk through patient areas. There would be so much particulate in the air, they would have to completely airlock surgery and recovery areas from the green spaces.
And that still won't help the patients and staff with severe pollen allergies. Get your chest stitched back together after invasive heart surgery and then blow it back open again with a sneezing fit on the way back to your ward.
That... is nonsense?
The surgery part of my local hospital has like three gardens that the patients freely use and nurses sometimes pass through for a shortcut.
Unless you're specifically opposed to plants in the hallways. Which the hospital also has, there's potted plants all over.
Hospitals are that drab partly as cost cutting not put of pure patient concern.