This doesn’t solve the problem of knowing which ones are guest towels and which are in use by housemates. Also, assuming that it takes at least a couple hours to wash and dry all the towels (realistically more like seven hours, given the large number of towels), and that each housemate only has one towel, this strategy would mean someone can basically just unilaterally decide that no one gets to shower for the better part of a day.
This doesn’t solve the problem of knowing which ones are guest towels and which are in use by housemates. Also, assuming that it takes at least a couple hours to wash and dry all the towels (realistically more like seven hours, given the large number of towels), and that each housemate only has one towel, this strategy would mean someone can basically just unilaterally decide that no one gets to shower for the better part of a day.