I am sorry to have offended you. It was not my intention, but I sometimes struggle to get my thoughts written out/represented clearly. My apologies.
Thanks for the apology. Let me see if we can dig out of this rut

I am going to attempt another explanation. If you want to learn, great. But if you just want to debate it, I'm not interested. These are facts, not theories
@txav8r summed it up pretty good (as usual

) There are a few different topics intertwined here. Regarding the compartment drain plugs, most of the time when there is nothing otherwise wrong with the boat, it doesn't matter much if they are in or out. Personal choice really. But I think its safe to say the general consensus (which was the original question I believe) is boat in water, plugs in. Boat out, plugs out. Of course that is a generalization. If the ski locker fills with water, well of course pull the drain plug to drain it. Nobody says it has to absolutely stay plugged at all times while on the water.
I see your train of thought in the bathtub analogy and I don't know how else to say this, but it is flawed. When it comes to extended buoyancy in an emergency situation, the plugged compartments do make a difference. Its absolutely possible for an open-at-the-top compartment to fill (but not overflowing) with water and the boat (or tub) still floats. This was the situation with the Titanic. It could still float with some number of (I believe it was 3) flooded compartments. The iceberg cut a slice in more (4 or 5 ) compartments and that simply exceeded the design limitations. In the bathtub analogy, it all depends on how big the compartments are. I'm not sure where the 10" came from, but that could be plenty if the compartments are not too large. You mentioned displacement, so I know you have some of the concepts. But here's the part you're missing: as long as each compartment holds no more water (in weight) than the weight of the compartment itself, then it won't continue to sink and it won't spill over the top flooding the next compartment. I wish I could draw a picture of the bathtub. Picture the Titanic with its walled (but open at the top) compartments. Now instead of an iceberg that sliced through the side of 4-5 compartments, lets say there was a torpedo that put a big hole in one compartment. That compartment would have taken on water, but only as much as the weight of that compartment itself. Water would rise to a certain level, but as designed, it would not be enough to reach the top. It would have stayed afloat. So would the bathtub. Both the Titanic and the bathtub would continue to float with a hole in the bottom of one compartment even though all the compartments are open at the top. Our boats are the same - as long as the compartments are plugged. If the Titanic had open doors in the lower level of all compartments (similar to having all drain plugs out), just one hole in one compartment would eventually sink the ship
My point about the cleanout tubes is that they are themselves a small compartment with an open top. I mention them because I though it was an easy-to-see example of this principle. When you remove the cleanout plug, you are opening a big hole in the bottom of the boat. Water rises in the tube only high enough to match the water level outside the boat (which is determined by the weight of the boat and the weight of the water it displaces). The water rises no higher and does not spill over the top of the tubes (not counting the splash in the face you get if the water is choppy

). Imagine now if the cleanout tube had a drain plug at the bottom of the tube that drained into the bilge and you left that drain plug out. Now remove the cleanout plug. It would not be good. The same principles apply to all compartments. Individually, each compartment does not hold enough water to weigh the boat down to the point of sinking or flooding over the top. But if all the plugs are out, you have one big compartment of water that will be too heavy for the boat to remain buoyant.
Besides all that, its not like the engines will instantly die as soon as water touches them. Its only if the water gets up to the top of the engines where the air intake is. Now here I'm going to speculate (theory, not known fact), but its very possible that if you keep the engine compartment plugged. The water may only fill up to a point just below the intakes. Yeah I know its still a scary thought, but the less water you allow into other compartments, the less deeper you will sink in the water and the lower level of water in that one contained compartment.
Hopefully this all sheds a bit more light on it for you

If it does, then you may owe me a few beers
and if not, then its not the end of the world either. I'm not trying to convert anybody to my religion.