Where do I make that assumption Michael ? Answer ... I don't. I assume the same power output for the hiker and the biker

Bas assumption. It takes more energy to propel the bike & to travel farther.

No Mike, basic fact. That is how bicycles work. They translate more energy into forward motion than walking so you can travel further for the same amount of energy.

The power source is one person; whether walking or riding.

Sure, the rider may be fitter and produce a bit more; but it's not the orders of magnitude you're constantly trying to push.

So they are travelling different routes, making them incomparable.

Complete non sequitur; we're discussing impact.

The energy input can't be the same, since the biker has more weight to carry, & farther to travel. You are assuming what you are trying to prove, which is blatantly dishonest. No surprise there! That's what mountain bikers ALWAYS do. Vandeman STILL 1000, mountain bikers ZERO.

Grow up. Read a physics book. Learn something.