Hard to control water temperature in shower
I figured out the problem: insta-hots, or what are called "tankless" hot water systems, have a pressure drop across the heat exchanger. If water is fed to both the cold and hot line at the same pressure, then there will be a pressure differential between hot and cold, the cold being higher. If both supplies are going to a common valve, then the cold will back into the hot supply. This can cause weird variations in shower temperature. For example, if a shower is started and the temperature is set, it will creep colder and colder because over time, more cold water creeps into the hot water line.

To solve the problem, it is essential that the pressure of the hot water coming out of the tankless system matches the pressure of the cold water system.