Go on then Einstein, show the maths to prove this.
Basic inline water heaters prove it. If it were so much faster, we
would have 3kW inline water heaters. As it stands, that it not the case.
Sure, as you increase power, you get more work done. But you also lose
more of that heat as well.
What it really comes down to is the diameter (and length) of the coil.
Since both 1kW as well as 3kW coils BOTH reach temperatures far above
the boiling temp of water, it would seem to me that you would foresee
some point at which there are diminishing returns from the amount of
energy one dumps into those coils over the return of heat imparted into
the water.
I'd bet that a larger diameter coil will heat the water faster than a
smaller diameter coil, for any given equal wattage, and the reason is
that the coil surface area is so much larger, yet it's surface temp is
very much the same.
So to me, the ideal heater for water would be one that does the job
with the least amount of energy in a reasonable time.