You are absolutely right on the hydro's being a supplied component. As are the motors, tires, wheels, bearings, clutches, electronic components, Etc.
I come from an industry that uses heavy orbital drives, pumps as well as various other hydraulic components. Even in this industry our equipment is a conglomeration components from various manufacturers. We try to stay with in the manufactures recommendation for fluids for the warranty implications, but be mindful that we relied heavier on oil testing for wear along with oil breakdown but let me assure you from dozens of test results there is a difference in synthetic fluids. With all of that said maybe we should be sending oil samples in even on mower hydro's to see the performance of each fluid in use (a small price to save a high dollar hydro), there are numerous synthetic fluid manufactures out there and even some petroleum super refined fluids as well additives in each are what defines one from another. The three biggest enemy's of a hydro system is lubrication value, contamination/filtration and heat, each play a large part in their life span.
I guess the reason I have confidence in the Hydro Max fluid is years ago on an older 1600 Grasshopper I was having problems with my left side hydro (lagging behind the right) so I replace the petroleum fluid with Hydro Max and bought myself four more years out of the unit, it did make a substantial difference. Would have another synthetic worked? Possibly/Probably?
The only thing I can go by at this point is after using up three Grasshoppers I have never bought a replacement hydrostatic drive. I'm sure many other owners can report similar reports and success stories that have worked for them, so this has been mine.