Air density is based on pressure and temperature. Pressure alone is only part of the equation.
Hot air molecules take up more space than cold molecules. If the pressures are equal, a cubic foot of hot air will have less oxygen molecules in it than a cubic foot of cold air, simply because you can't fit as many of the larger (hotter) molecules into the same space.
So if you have 30 psi in your manifold, a hot 30 psi charge (small turbo) would have fewer O2 molecules than a cool 30 psi charge (bigger turbo). If you add more fuel molecules, you need more O2 molecules to balance things out. Pressure, in itself, isn't what keeps our egts down. It's the amount of oxygen molecules.
As a small turbo overspeeds, the friction between the air and the blades, the quick ramp up in pressure, and probably even the blade tips approaching sonic speeds will superheat the air charge. The larger turbos can keep the speed down to move the same mass of air, which in turn will keep the discharge temps down.
Using the water hose analogy is a little confusing since liquid is incompressible and doesn't really follow the same rules as a gas.