I'm quite squeamish unfortunately and the thought of something being put into my eyes makes me feel "peculiar". It's the same reason I can't consider contact lenses as the thought turns my stomach! My eyes are also fairly sensitive. If my hubby's cooking something strong or with onions, my eyes will start streaming and itching from the next room, even with the door closed.
I know they can and do, do the screening without the need for drops. I don't want to have the stinging sensation and quite possibly blurred vision afterwards.