It's one of the "benefits" of 4.3.
If they're user apps you can uninstall them without rooting. (Settings/General/Application manager.) If they're system apps you have to be routed. Be careful, though - something you think has no business being on a device of yours may just be something that makes the phone complete the boot process. Remove it and the phone stops working. (The way Android is going, it looks as if more and more of the operating system is going to be apps. So if they have to, say, totally redo how LTE works, they don't have to issue an OS update and take weeks slipping it out to users, they just issue an update to the "LTE app" and a few MB per user fixes everything.)
With me it depends on the value of the phone. When I got a Precedent (they sell new for bout $40 now), I rooted it, put in ROMs, experimented all over the place. If you smoke, you blow that in a week or less. With my Note 3s? $700 and change isn't something I want to watch go up in smoke. I don't need to remove the bloat - with all the junk I''ve been playing with and haven't uninstalled yet, I still have just under 22GB free internal storage. And a lot more on the 32GB external card. There aren't any root-only apps I'd run on a daily basis. It might be interesting to play with some of the Xposed modules, but not $700 interesting. I can do GPS analysis, wifi analysis, 2G/3G./4G analysis with non-rooted apps. I can even capture wifi signals (there's a wireshark equivalent for Android) without rooting. I've got EXIF-stampers, cameras that are almost as feature-loaded as my old Canon 35mm, I read all the magazines I'm interested in on the phone - and no root. My finger isn't worth $700, so these phones stay stock until something comes along that's going to earn me a nice vacation with enough left over to buy a new phone if it goes and Samsung won't honor the warranty because of the su file I copied to it. I guess I agree wih your girlfriend.