@bryesh
Again, some of the assumptions you are making (or not making) about this complicated system appear to me to not be quite right...
Q_mech2 > Qmech1 could be true. Remember, the engine drives the water pump, too. If you remove the thermostat, it's pumping more water, although against a lower pressure rise. The water pump might be drawing more power, or it might be drawing less power.
eta2 < eta1 could be true. As I asserted above, the coolant is going to suck more heat out of the engine if it's flowing faster. Therefore, the engine becomes more inefficient - more of the heat from the burning gasoline is going into the coolant. Even if T_coolant2 < T_coolant1, that might mean that the temperature of the air going into the engine is lower, meaning higher pumping losses at steady-state part-throttle. Thus, eta2 < eta1. A real gasoline engine is way different than the Otto engine from thermodynamics class.
Q_alt2 < Q_alt1 could be true. If the coolant is sucking more heat out of the engine, then it's also possible that less heat is going into the exhaust, oil, etc.
Any one of the above could be true, which could lead to the result that T_coolant2 > T_coolant1. Please understand that I am not saying that T_coolant2 > T_coolant1 on every vehicle. I am saying, "it depends", specifically on how much Q_mech, eta, and Q_alt change. In some cases, coolant temperature will increase. In other cases, it will decrease. Our members own experiences in this post show this.
Let me ask you a question: Let's say that your math is right, and removing the thermostat will cause the coolant temperature to DECREASE for every engine and radiator combination. What that means is simply this: you have proven that increasing cooling flow rate GUARANTEES that steady-state coolant temperature will decrease, right? If that were the case, why wouldn't engineers design the thermostat to have a 3-inch opening? Why wouldn't engineers design the hoses to be large, smooth, no inner springs, and flow tons of coolant? Why wouldn't engineers design the water jackets to be very smooth and well shaped for flow? Have you ever cut open an engine block or cylinder head and looked at the water jackets - they are terrible for promoting flow. Why wouldn't engineers design the head gaskets to have huge holes to allow lots of coolant to flow through them? Helk, if increasing coolant flow guarantees lower coolant temperature at steady state, then let's make everything in the cooling system flow well! If we do a good enough job, then we can decrease the size of the radiator to the size of a heater core! Man, the styling department would love that! So, why don't engineers make any effort to improve coolant flow through the engine? Why do they use small thermostats that don't flow very well when open? If simple equations proved that increasing cooling flow guarantees lower steady-state coolant temps., then engineers would already have been all over it, yes? And yet they don't seem to care... why?
Mike