Much of the actual power of a tractor comes from the gearing of the machine.
I have a car that has about 300hp, I have a fleet of diesel trucks that have about 175hp. Which will haul more weight? The diesel trucks have the ability to pull loads in the 30,000 pound range, but my Avanti convertible would likely burn out the transmission trying to move that amount. This is very similar to the garden tractor versus CUT question.
There are also some serious torque issues involved, as previously mentioned. The garden tractor will have minimal torque compared to the CUT, which effectively means it will be unable to transmit the power to an implement or the wheels or both. For example: consider a high speed drill, they typically have very low torque and it is pretty easy to get the bit stuck in a fairly thin piece of metal when drilling, but a drill with greater torque and lower power can easily drill through the same material without binding.
There are also some additional issues as well, such as transfer efficiencies. A hydrostatic transmission is slighly less efficient than a gear transmission and consequently a tractor with a HST tranny will put 1 or 2 hp LESS to the PTO than will a tractor with a GEAR transmission. That said, your uncle likely has a glorified fan belt that drives off a spindle at high speed and is reduced down to run the rear wheels and the mower deck. SHORT OF MENTAL TELEPATHY, it is probably the least efficient way to transfer power I can think of.
So, a garden tractor may need more power simply to do less work because of a combination of the above factors because many things conspire against its abilities. And most of the reasons are cost related. It is often cheaper to up the HP of the tractor than to put in a more efficient transmission, gearing, etc.
Further, much of the reason I think (MY OPINION ONLY) for garden tractors having such large HP engines falls into the TIM TAYLOR line of thinking. If 12 hp is good, then 24 is TWICE as good! ARG! It is simple marketing. Give the caveman more power and stroke his ego.