So you want to stick a rod in the ground, and use that as a ground instead of the ground wire. Let's see how that works.
Electric current travels in loops, and we are concerned with two separate loops. First, natural electricity (lightning and ESD) - it's sourced from the earth, and wants to return to the earth. Ground rods are great for this.
Second, human-made electricity (mains power). This is sourced from the generating plant, or in the local loop from the transformer. Since it's an artificial source, it wants to return to that source - not the earth. For that, you need a ground wire back to source (the service panel).
Ok, so without a return ground wire, what happens when a light or tool develops a hard short from hot to ground? It should draw about 300 amps and magnetic-trip the breaker. so let's follow the amps.
- through the local grounding system
- to the shed's ground rod
- into dirt
Needless to say, if dirt could carry 300A, we wouldn't use wires! So the dirt will be unable to return the large fault current. As a result, the grounding system floats up to 120V. The next guy to touch a switchplate gets nailed.
The ground rod lets you do more
I really don't like the idea of an outdoor subpanel without a local ground rod. It's local for a reason, and that reason doesn't go away without a structure there.
For what it's worth, however, you can put a lot more power up that expensive wire. There would be no trouble provisioning a 240V/50A, 240V/100A or 240V/125A panel up there on those same wires... especially if you already have 480V, 575V or 600V in the building. Come on back and ask if you ever get to the point of needing that.