I wonder if anybody has ever tried to do a study on where "peak efficiency" lies on this spectrum (i.e. how much do you need to allow people to goof around, such that the subset of their time they spend on being productive yield the most value).

Well, the good thing is that generally that 90% of disease can make that real work much more efficient. After a few years of 90% disease, you're probably able to knock out the equivalent of at least 60%-80% of real work in just that 10% of time.