Skinny tires are used on UCI time trial bikes for one reason, aerodynamics. The large diameter front wheel is the farthest forward part of the bike and reducing the width of the tire cuts down the overall frontal area a significant amount. When fairings are illegal, cutting down on frontal area is the main way to go faster. The type of time trial bikes which set records are doing it on smooth velodromes so there is no reason to use a wider tire for handling or safety reasons. Some track tubulars are so thin they are only used for a few rides.
Operating costs are no object for an hour record attempt time trial bike.
Over the road time trials tend to use somewhat wider tires for added comfort, protection, and control, though still relatively narrow as aerodynamics is still highly important, generally far more significant than rolling resistance which wider tires are known to reduce. I didn't need the fat tire seen on the typical pot bellied recumbent rider of the time. After extensive recumbent riding on tires from 19mm to 54mm width I have come to a fairly clear conclusion. For the average rider on average roads a recumbent needs wider tires than an upright road bike. The primary reason is because the recumbent rider can't deweight the bike for going over bumps and other road hazards.