All true. But you also need to remember that Henry's law comes into play reducing the solubility of gases as the water heats-up. The upshot is that as the water approaches boiling point all of the O2, N2, CO2 (etc) are forced out of the liquid. The bubbles you first see on the bottom of a pan of water as you heat it are predominently dissolved gases coming out of solution and not steam. The steam bubbles only appear when areas of the liquid are sustained at boiling point.
If you want to see a demonstration of this, boil some water and let it cool for a little while - preferably closely covered, say in a lidded container filled to the brim, so as to prevent lots of gas being re-absorbed by the water. Then boil it a second time and you'll see far fewer bubbles on the way to bulk boiling.
Batroost (from a place that makes 2 tonnes of steam a second - what's that in pounds per hour?).