A fulcrum is a pivot point. It can't be longer or shorter. The crank arm is the lever. (That much I'm pretty sure of.)

That said, the relationship of the crank arm length to power transmission is murkier than it appears to be. There are, in fact, four levers in play: the crank arm, the chainring, the sprocket, and the rear wheel.

Altering the length of any or all of those levers changes the level of pedal effort required to travel a given distance.

I always found this concept hard to get my head around, until I thought about my experiences using different gear ratios while climbing trails off-road. When I was climbing a steep trail under muddy conditions, choosing the right gear and maintaining the right pedal effort were crucial. You can just as easily lose traction (i.e., apply too much force) with shorter cranks and a slightly lower gear ratio as with longer cranks and a slightly higher ratio.

And, about "explosive sprinting power": one very successful sprinter I know who won national titles on the track over a couple of decades once mentioned to me that his secret for success in criteriums was that he always used a 50-tooth chainring. He and the other racers would usually be in the same sprocket on the back wheel, but he'd have just a bit more mechanical advantage.

Of course, some other rider might have slightly longer cranks, but that would just mean that the difference in mechanical advantage between the two was altered. Depending on the math, the longer cranks might give that other rider the edge, or they might not.

That was back when everyone else was using a 52, 53, or even 54 ring. He didn't alter the length of the crank lever arm---he altered the length of the chainring lever arm. Same effect.

In other words, it's all about the distance the bike travels versus the distance the pedal travels. The crank is just one more lever in the system.

Of course, riders with longer femurs might find longer cranks advantageous, although some recent research isn't even clear on that point.

About the math:

Sheldon Brown recognized many years ago that gearing calculations that don't incorporate crank arm length values are incomplete. He explains why and how to remedy the problem in his Web page titled "Gain Ratios-- A New Way to Designate Bicycle Gears."

From that page:

"What about crank length?

"All of these systems share a common inadequacy: none of them takes crank length into account! The fact is that a mountain bike with a 46/16 has the same gear as a road bike with a 53/19 only if they have the same length cranks. If the mountain bike has 175's and the road bike 170's, the gear on the mountain bike is really about 3% lower!"