Having spoken with a variety of P@H staff over the last 6 months, I can only suggest that you can take what they say with a pinch of aquarium salt. Their points system, to be fair, does seem relatively valid. The problem would be in aiming for the most fish you can fit in your tank, which may work well enough...until it doesn't. The closer you get to that stocking 'limit', the more fragile the ecosystem in your tank can become and, if something goes awry, then things can go pear-shaped, very, very quickly. You lose room to manoeuvre.
Your fish would 'probably' not suffocate at your current stocking levels, but plants photosynthesise during the day, when the lights are on and produce oxygen. (This includes your algae). No plants means less oxygen in the water and, obviously, oxygen in the water is A Good Thing.

That said, with no plants, there should still be enough oxygen diffusing into the water through the surface. (This is why many of us look at a tank's surface area when considering stocking levels). Agitating the water surface with the outflow from your pump and/or passing bubbles through the water from an airstone, will increase the surface area.
As you've seen, you'll see plenty of tanks without plants and such tanks do tend to have their stocking levels carefully managed.