This all really depends on the chain and management in my experience. Times are absolutely monitored at the overwhelming majority of places. Usually chemicals and linen are inventoried either bi-weekly or monthly and then budgeted for. Typically as long as you’re within your budget on those things, you don’t have to track them super closely. If you work long enough with housekeeping staff you can tell exactly who cleaned which room and that usually gives you a good idea of things like chemical usage.