I have now resolved my problems making a recovery drive for my brand new Dell XPS 15 9570.  Here is the low down:

I started with the recommended 16GB USB sticks, brand new from Kingston.  I got the same result on three attempts.  The software chuntered away for over an hour and a half, and then gave me a message something like 'Failed to create recovery disk' with no way out other than 'Finish'.  Examination of the USB sticks showed 13.6GB used and 777MB remaining free.  They were in FAT32 format.

After advice from Dell Support, I tried a new 32GB PNY USB (which had an activity LED).  Formatted NTFS as advised.  This time the software ran for over two hours.  The progress bar showed full, and the sweeping graphic across it had stopped happening, but the activity light on the stick was still going.  After another 20 minutes, I gave up and hit the 'Cancel' button, as I believed it was stuck in a loop and would never finish.  This time the USB stick had 23.1GB on it, and some 5GB or so still free.  I had no confidence that this would work as a recovery drive, and wiped it with a fast format.

Today, I re formatted the PNY stick again, with a long format (not the quick format) to NTFS.  Then I tried again.  My wife took us out grocery shopping while I left that running.

Approximately 3-1/2 hours later I looked and was surprised to see that it had finished, and the message on the screen said 'Successfully created recovery drive'.  I hit 'Finish' and then had a look at it.  It has 23.9GB  used, and 4.97GB free.  It is formatted to FAT32.  

So, I had been so near to completion yesterday when I gave up on it.  Obviously, there is a lot more on there than just Windows 10 Home, and all the Dell stuff has been backed up as well.  Dell support assure me that their 'enhanced software' and security and Windows activation are all on there.

So, if you have trouble making your recovery drive, use a much larger USB stick and leave it running until it tells you it either failed or completed.  Don't interrupt it, even if the progress bar shows full and no activity seems to be happening.  So much for a 16GB stick.