Always a touchy subject, and always good for a laugh.
All I know is my 445's (same transmission as a new x7 series for this discussion) makes an unpleasant howl when I drive it under load at anything less than 3/4 throttle. So, it's always at WOT or at least close when the tractor's moving. The transmission sounds MUCH happier, and responds better. The hydraulics (FEL and power steering) also work much better at high rpm, when they get full flow and pressure.
I had a 425 (carb engine, similar to a new x710), that had well over 3000 hours on it, still ran great, pto clutch still perfect, transmission still strong. It was owned by a school and had the snot beaten out of it, but fluids always changed on time. The engine and tranny had never been taken apart, except the plastic cam gear replacement. Everything else was worn out, rusty, or broken, but the engine and trans were fine. Front end was so worn out you couldn't even drive in a straight line.
Now, my 140 seems perfectly happy to putter around at any engine speed. The hydro doesn't even groan under load at idle. Different machines act differently. There's not one common part between them, so why should they be operated the same way?
To the O.P.'s last point, your transmission does have a cooling fan. It's the same one that cools the engine radiator, because there is also a hydraulic oil cooler in there that cools the transmission oil. If your transmission is overheating, it will also cause the engine to overheat, and the temp gauge on the dash will go up to the red zone. FWIW, my gauge has only gone to the red zone once, and it was mowing on a hot dusty day and the radiator got clogged. A quick clean-out, and it was back to running cool as a cucumber.