Ethan the higher the pressure on the cap the higher the coolant temperature in the block can be before it boils. Once it boils it stops being a coolant, and as you know from watching a pan of water boil the bubbles form on the surface of the pan first.
Those bubbles act as an insulating blanket that means the heat is prevented from moving past that barrier so you can get hot spots in the engine that can promote deadly detonation. Detonation is the auto-ignition of the fuel because the temp exceeds the octane rating of the fuel. You hear it as pinging or a rattle in the engine. Detonation breaks your stock cast pistons apart (which is why race engines are built with forged pistons; which are not stronger than cast pistons, they just stay in one piece when they die).
The stock pressure cap rating was 16-18 pounds of pressure. The 13 is offered because in an old car the radiator AND the heater core are soldered together. That soldered joint is weak. Put too much pressure on an old solder joint and you have a coolant puddle on your passenger side carpets, or an over heated engine as all of the coolant is pushed out past the joint that failed.
Aluminum radiators used in modern cars and race cars are not being used because aluminum is a better conductor of heat, it isn't. The factory uses an aluminum radiator in modern cars because aluminum is today cheaper than copper is to buy (because we have already retrieved all of the easily available copper on the planet). Racers use aluminum radiators because they are welded together not soldered. That makes them stronger: as such, they can increase the pressure on the coolant by way of using a 24 pound cap. Also because aluminum is stronger the radiator tubes can be made bigger. The tubes are 56% bigger which increases the surface area allowing two one and a quarter inch tubes to cool the engine better than four three eighth inch diameter copper tubes can even though copper is the better conductor of heat.
As to the thermostat, I run a 160 in my big blocks to decrease the temperature of the heat soak in the Otto Cycle. From a Thermodynamics point of view, the higher I can drive the temperature in the combustion chamber by increasing the static compression and limiting the drop in the dynamic compression in cam duration the greater will be the difference in the two extremes which increases the horsepower potential in the thermodynamic cycle. The factory runs a higher temperature thermostat to reduce emissions (modern thermostats are 210 degrees).