Yes it is annoying quirk that you can't back up your home screen settings, settings etc. It should be possible to sync any and all settings to a PC and restore all or any to another phone of the same model. It's the one thing that Apple have got right.
While a Nandroid back up with a rooted phone will take a "snap shot" of it at that time I would be rather wary of restoring a Nandriod to a different phone to the one it was made on (That one would have to be rooted as well). Nandroids can be pretty temperamental things; for instance never change their folder title it borks the Md5 checksum rendering them useless.
Samsung Galaxy Note 3 SM-N9005
ROOTED STOCK FIRMWARE PHILZ TOUCH RECOVERY
"The only foolish question is the question not asked"-Anon