Rather than a knee-jerk ‘just ban everything’ reaction, would there be a halfway house that could work? Crew distribute towels as normal, but rather than collecting in using the blue tea trays, find an alternative. Such as taking a plastic bag through the cabin into which customers are asked to drop their used towels. This can then be sealed and binned.
I get that crew don’t want to be handling them... I probably wouldn’t really either. But I can’t help but think an imaginative solution could be found, given that people do like to be given towels and other airlines will continue to offer them.