While it is true that our systems are designed to run at 13 pounds of pressure, if the hoses are in good shape, that is to say replaced in the last 5-10 years, they are good for the 16 pounds of pressure. The heater core is an area of some risk. If it has never been changed it may push it over the edge. If it has never been changed it may fail at any point in time. If I were running a 40 plus year old car with the original heater core I would change it. If it were not my daily driver I would at least unhook it and bypass it until I could change it.
if the heater core has been replaced and is in decent condition, a 16 pound cap shouldn't hurt it.
and finally there is the radiator . . . shops pressure test them well above 16 pounds with no ill effect. If the condition is marginal, stay with the 13 pound cap and save your money for a new one. If the condition is good 16 pounds should be tolerated well.
In 30 years of hotrodding, I have changed every thermostat to 16 pounds or higher and have had many friends do the same. I've heard the cautions, but never seen it develop into anything, but then again I've always maintained my cooling systems with good hoses and flushes every few years and good coolant.