Downloading an Xbox One profile to an External Hard Drive

No.

Microsoft removed this possibility on the Xbox One due to the Xbox 360 Mass Profile Modding, and they typically don't take up more than 16 MegaBytes of space for a 1 000 000 G Player. Xbox One minimally comes with a 500GB Hard Drive built in.

External Drives lose data much more easily than internals as well, accounting for quite a lot of "AAAaaaAAaHhhH my profile is corrupt!!!11!1" support tickets. ((Yes, there was a thread with that name a few years back on the forum.))

If their profile is indeed taking up a lot of space, somewhere along the line it has become corrupt-or they frequent a game that repeatedly adds bloatware to their profile itself.

Xbox system and updates usually take about 25% of your available storage, which you can do nothing about.

The biggest offenders are typically "But I paid $60 for that!" games, followed by games in general, poorly built apps, and Xbox general software instability.

Don't try this at home kids-but there is theory floating around that there is a way to measure profile size using a Windows 10 PC, and/or OneDrive; assuming you no longer have access to a 360.