The first time I heard about it at an airside airport lounge, I did a double-take because I couldn't believe they wanted money for towels -- but that was not an airline-operated lounge. And that was years after I had to do a double-take when I first came across an airline lounge where showers were available but they weren't available to me even as I was able to use the lounge otherwise. The crime with this "no-shower" "penalty" at an airline lounge? I had the wrong FFP membership with status allowing me access to the lounge as an economy class passenger.

Every shower-having airline lounge which I've used for a shower in the current and previous decades -- access granted based on airline class of service and/or FFP status -- has granted me shower access + towels for no surcharge.

It's because they tend to have access to a lot of cheap labor to do these kind of things. But it's also because they have a lot of "labor class" employees from the LDC who don't have much if any familiarity with modern conveniences at airports and may misconstrue matters; and when they don't understand features/purpose, it can mean a mess for the cleaning staff and the public at the airport while also potentially being an embarrassment for the unaware users of those facilities.