"Drats! But part of me still thinks why isn't it like when you put your thumb over the end of a hose, you trade some volume for some pressure. "
You need to look at what is really happening. Without the thumb over the output orifice, there is no back pressure in the hose. All the water pouring out the actual end is no longer under any pressure... as there is no restriction here (there is in the hose itself from wall friction etc).... so the water falls out, pushed only by the water behind it trying to get out too.
When you restrict it, you build up back pressure. If you block it off you will build up full pressure.
So if we had a pressure gauge tapped into the hose say 1 foot in from the outlet, with no thumb, we get very low pressure, but max volume, but when we clamp the end of the hose, we get the static high pressure, and no volume..... so we can use anywhere in between those two states to do things.
If we partly open the outlet (spray a bit about) the pressure now in the hose tries to push whatever volume of water it can, out through the smaller orifice. It cannot push with more pressure than the static pressure (blocked hose).... and will always be less once we release water out.
Friction losses in the hose (result of velocity of the water and hose diameter ) work against us too.
So the smaller the outlet hole, the greater the pressure can build towards static max..... and the more pressure available to push the max water out of the hole.... so it moves faster.
But the pressure can never be higher than the static pressure (except for inertial change... ie the instant you block it..... you must decelerate the water that was moving. This can be used for ram pumping to very high pressure.).
Nothing is for nothing in this universe.... so for turbines we use jets to get the best combination of water velocity driven by back pressure. Restrict too much and we get high back pressure..... but we lose the mass.
If we don't restrict enough, we lose the velocity needed to turn the turbine fast enough.... but you cant beat the turned off (static) pressure. You can balance the pressure:velocity part to get what you need, but not pressure max.... the more you open the jet, the less pressure built up in the pipe to push the water out with.
just more mud....................oztules