Westfalia hitch wiring confusion

I’m planning on ordering a Westfalia tow hitch with the dedicated electrics kit. After searching around on TDIclub I see a lot of write ups on how to use a 7 pin euro with a 7 pin USA connector. I’m not really sure why I would want to do that. The trailer I’m planning on buying has a 4 pin flat style connector. Can’t I Just use this Reese 7 pin Euro to 4 Pin flat adapter? https://www.amazon.com/Reese-118710-.../dp/B00IE41DIC
I’m planning on adding brakes to the trailer. Is that why I would need the 7 pin? All the write ups ive seen involve coding the module or ECU. Wouldn’t it just be easier to convert the trailer from 4 pin to 7 pin euro? Or run the trailer brake controller separately? I’m I missing something?

TL,DR. Can I use a Westfalia 7pin wire harness and a Reese 7pin euro to 4 pin flat adapter and have all my trailer lights work?

Bump......

If you're going to do trailer brakes, you want the 13 pin Westphalia, because it has a pin that can be used as a trigger wire, going to your brake controller, and then coming back out (blue wire) to the brake connector on your US 7 pin round.

And that is correct - you need VCDS to code the module, as it connects to the CANbus. It's not hard, though the hard part for me will be moving the wiring from my 2010 to my 2013.