As a pot of water is heated and its temperature goes up, more and more water vapor is produced above the surface.
That’s because more and more of the surface molecules gain enough energy to leap off into the air. The increasing amount of water vapor carries off an increasing amount of energy that could otherwise go into raising the water’s temperature.
Moreover, the closer the water gets to its boiling temperature, the more energy each water vapor molecule carries off, so the more important it becomes not to lose them. A pot lid partially blocks the loss of all those molecules. The tighter the lid, the more hot molecules are retained in the pot and the sooner the water will boil.
Your point, that a lid increases the pressure inside the pot as in a pressure cooker, thereby raising the boiling point and delaying the actual boiling, is correct in theory but insignificant in reality.
Even a tightly fitting, hefty one-pound lid on a ten-inch pot would raise the pressure inside by less than a tenth of a percent, which would in turn raise the boiling point by only four hundredths of a degree Fahrenheit.
You could probably delay the boiling longer by watching the pot.