I agree Apple usually puts in warnings but updating a device is different since a device is somewhat stand-alone, particularly with Apple's increased move towards iCloud services. Additionally, some computers can be upgraded to OSX10.8.5 or higher which is required by the newer iTunes, you just need to do that. Those that cannot are officially vintage or obsolete and therefore "unsupported" which means don't expect anything when using such a computer. You can continue to use them (my Mac is 13 years old) but it is 100% on you whenever you do any changes.
Workarounds:
Backup to iCloud
Download purchases directly from the iTunes Store, particularly movies.
Subscribe to iTunes Match or Apple Music to put your other music in iCloud to sync from there.
Use other services such as Dropbox to transfer other files.
Use iPhoto, PhotoStream, or Image Capture to download Camera Roll items.