STP is an additive for gear lubrication and hydraulic fluid is designed for pressures and flow applications. I fail to see the use of it in hydraulic systems except maybe in older systems that use lubricating oils for operation.
Likewise, to test this you should be able to add hydraulic oil as a supplement to your engine oil on a new car and see how it runs! I would not risk this and you wouldn't either. Better to leave it the manufacture recommendations and be done with it.
I agree. There is a phsychology to their methods- we think that adding a little of this or that will increase life, power, and reliability. But, the manufacturers spend millions on R&D, and their recommendations are invariably the best route to go.
My wife has a 2000 Ford Windstar. I was going to drive it to Homstead, FL, and was topping off all the fluids. I knew that in modern vehicles, you don't mess around with viscosity- the passages and holes are smaller and more precise, and if you change the viscosity that was engineered in the engine, you are playing dangerously. There was a bottle of STP oil treatment that just called my name, though. I added some, thinking that it would be helpful on a long distance, fast trip to Florida (we were picking up a Haitian pastor, turning right around and coming straight back). Wrong. I messed up the bearings in the crank position sensor. Now, this is not about STP, or even to diagnose what may have happened- the point is, when we second guess the engineers and designers, then we take the responsibility on our shoulders. Fuels and oils are very complex- even with deep investigation, we are stabbing in the dark when we add stuff to the oil and fuel. Some things are harmless- time proves that. Other things are not.
You can do whatever you want- it's your tractor. But, I would ask myself this- why do I want to add STP to my hydraulic system, and what do I want to accomplish by doing it? And, how do I know that I am accomplishing something, instead of harming something?
Like Bulldog said, using high quality, approved oils is the route to go.