Brand new Microsoft Surface Pro 4 - can't create a Recovery Drive!?!

I just bought myself a Microsoft Surface Pro 4. After switching it on and going through the initial setup, one of the first actions I want to do is to create me a recovery drive (on a USB stick).

So I start the Recovery Drive wizard but after a minute or so of "Please wait..." I get:
"We can't create the recovery drive
A problem occurred while creating the recovery drive"

Hallo, Microsoft? WTF is this supposed to mean? Why can't I create me such a safety net on a brand new plain vanilla SP4? I haven't done or installed anything, yet, that could possible interfere with that process. So why is this not working as one would expect?

And why is there not the slightest hint WHY this is not working or what kind of error occurred here and what one could possibly do to fix this?

I hate those generic error messages without any explanation or error code

Meanwhile, did you try another USB drive just in case?

I did so after googling on that subject but that didn't help. The process then continues and shows the drive. I select it and click Next and then it endlessly hangs. I killed it after ~2.5 hrs. because IMHO it can't possibly take that long to write those files onto the stick.

Re. your response: That's e.g. one of those things that I would expect as part of the error msg. that it clearly states: "need a FAT32-formated stick" (or similar) not just "an error occurred...".