Tiguan :: Going Downhill In Automatic Mode And Auto-downshifting

I was driving around some very steep hilly highways recently. I have tried this in both cruise control and normal coasting.

I noticed that the Tiguan will automatically downshift when going down a steep enough incline and a certain higher speed is automatically reached. Whether that is based on what was set by your cruise control, or even when letting the car coast down by releasing the gas peddle, it will still reach a point of downshifting automatically.

What I hate about it though is that this downshifting causes the engine to suddenly rev very high RPMs. Its also pretty loud at that point. That's bad for the transmission system right?

Usually in automatic mode driving, gear shifts up at around 2,500 RPM (mostly around 2000 RPM point). But when you are going downhill in a steep incline, the Tiguan automatically goes to a lower gear causing the RPM to shoot right up. I've had mine go up to 4,000 RPM downhill and the engine screams and spins really fast as you can clearly hear. It of course does the job of keeping the car at a certain speed, but is this bad for the transmission?

I mean, I prefer pressing on the breaks to control speed downhill. Break pads are cheap and easily replaceable. Transmission strain and failure is a whole other business. So I would prefer the strain be placed on my breaks and not my transmission system for the purposes of controlling speeds downhill. The latter failure mode will be the case if they rely on the transmission to control speed downhill.

So what is a "happy RPM" for the engine anyway? What RPM is the 2.0T engine at its most efficient?