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On my tires, max is not stated on the sidewall.
When towing, I do start with the rears just under or at MAX COLD when cold.
Even when empty, there is no noticeable difference to taking them down to lower pressures. Am sure there is some scientific test out there that will show a difference of X inches or X feet stopping distance though. YMWV.
Also, am sure that there are plenty of ways that different people manage their tires. So, in this case, am not looking to claim which approach is best and am merely answering the original question
Are they mud tires?? Please show a pic of a DOT street tire that does not state max pressure, load range, and traction, tread wear, DOM etc on it.