Are you using the 64bit version of MC? Also please remind me which specific version of MC you are using. i.e. MC23.0.102?
I used to use this function and it worked fine. But I haven't used it in a long while since I only use an old iPhone to play music to calm my dogs at night. No need to update those as the dogs don't complain about the selection!
But I don't know if that function works on the 64bit version of MC. Handheld Sync didn't work on the 64bit version, and this is sort of related, so maybe it doesn't. But then we have this;
23.0.82 (11/13/2017)
15. Changed: Enabled support for Handheld devices which expose a drive letter in Media Center 64-bit (ie. USB thumb drives, portable music players or phones with a single storage volume).
So I just checked and Handheld sync to a directory on a hard drive works fine in MC23.0.102. So one way to get music on to an iPhone is to sync files to a directory on your hard disk, with conversions if required, then import these into iTunes and sync that to your iPhone. That process still allows you a lot of control over what you sync to the hard drive to then be synced with iTunes > iPhone. Better than just copying files to a directory for import into iTunes or something similar. Depending on your media file formats, the conversion capability alone makes it worth using.