I know there is no free lunch so I am missing something conceptually here
What do you mean by power?
Volts or watts ?
You are right that people are making this more complicated than need be.
Power is measured in Watts and is useable energy no different than heat (btu's) or light (lumens) or even calories and can even be converted from one of these measurements to another.
Voltage is measured in Volts and is the electrical "pressure" and can also be referred to as electrical "potential"
Current is measured in Amps and is the electrical "flow"
Resistance is measured in Ohms and is the electrical "opposition" or "restriction" to flow
The reason induced voltage is not simply "free energy" is because the resistance values will not change regardless of if it is step up or step down. Because the resistance values will stay the same, the power values will also stay the same. Another way to say it is the voltage may be higher in a step up but the result will be current will decrease because resistance doesn't change. That is why some were showing the formulas.
Eg. If the resistance value of the whole system is 35k ohms and the voltage produced is 10k volts you will have a current of 3.5 amps. If you were to now insert a (let's say 1:2 ratio) step up transformer into the circuit, your induced voltage will become 20k volts. But a transformer doesn't change the resistance of the whole system (in theory) so you still have 35k ohms resistance which will now result in a current of 1.75 amps. So to figure out the actual useable energy (watts) you multiply volts by amps.
No transformer: 10000 x 3.5 = 35000 or 35k watts
With transformer: 20000 x 1.75 = 35000
So now you can see that even though the voltage is stepped up, the useable energy is constant as many of the previous posters also said.
Volts = amps x ohms; Watts = amps x volts
Clear?