A friend who worked in a factory which laundered these "continuous" cloth towels (and hospital linen) claimed that these were more hygienic than either paper towels or air dryers.

This is a commercial web site, but it alludes to a study by the University of Helsinki:

https://ituabsorbtech.com/are-cloth-hand-towels-from-a-roll-dispenser-sanitary-2/

A common misconception about cloth roll towels is that they are on a continuous loop in the roll dispenser.

The reality is that there is no loop at all.  The towel is open-ended and the clean portion is stored in a bin at the bottom of the cloth roll dispenser.  The clean and dirty sections of the towel never touch. Once the towel reaches the end, it gets placed in a bin or drum for laundering and a new, clean towel is placed in the unit.