I won’t call any names here, but let me put in writing something I’ve been saying for years: unless you can mess with air pressure, you can’t increase the internal temperature of a boiling pot of water, no matter how much more power you add to the heater. Adding more heat only speeds up the evaporation process.
Similarly, when you’re boiling a dish in a regular (non-pressurized) pot, increasing the heat after the water (soup, milk, sauce) starts boiling CANNOT increase the temperature of the soup/water/sauce and it CANNOT speed up the cooking process. The only thing you speed up with this action is the water circulation inside the dish and loss through evaporation, so you’ll need to add more water sooner. All the extra heat energy added to a boiling pot of water gets used to break the inter-molecular ties and change the aggregate state of the water from fluid to gas (steam). This is also known as latent heat.
This is why it’s better to simmer things than to cook in an overflowing bubbly pot of hot water which can burn people and add incredible amounts of humidity to your kitchen. The only valid reason to increase fire on a boiling pot is when you are cooking meals which tend to stick to the bottom of the pot and burn – increasing the heat will speed up water turbulence as little bubbles of steam will keep moving the water and mixing food around faster. Otherwise, turning up the knob on the stove won’t speed a thing if the soup is already boiling, so save your energy.