Having a power limit is not the same as running at constant power. Why would you run at constant power with variable frequency? It would be wasteful. And how would it even work? How would you keep power constant while reducing frequency? Do you even understand what determines power consumption of a chip?
This is pretty much how laptops work. That's why CPU temperature can spike during initial boost to, say, 99 °C and then settle at 75 °C. A simple continuous power limit will achieve this. It's a pretty standard behaviour for laptops. Of course, if ambient temperature gets too high (or the heat exchanger gets too clogged with dust), you might trip a thermal limit.
Yes, it's possible to ensure that everybody has the same experience. Electronics have operating limits. There is a maximum temperature and you're not allowed to use the equipment when it's exceeded. If you cap your power budget so that your cooling can dissipate that much heat under the most unfavourable conditions, everybody should get the same experience. The disadvantage is that people with better conditions are going to leave unused headroom on the table. The cooling system would be able to take more heat in those circumstances increasing the power limit. There is no such thing as free lunch. Either you leave performance on the table or you'll have to throttle when conditions get worse. I guess fairy tales sound better.