Most if not all carrier-loaded bloatware can be disabled using the Manage Apps screen, no need for root to do it.
I've not rooted my Note 3, I see no need to do it. I need my warranty on the device.
Most warranties are only a 1 year. Inportant yes.
Most credit card will extend that 1 year, and to the best of my attempts to read fine print, there is nothing in those credit card extended warranties that mention anything about software or rooting, or anything such as that.
I opted, still not sure why, but since I paid full price for my Note 3, I got the vzw equipment protection plan. I read that thing twice, and nowhere could I find anything that hinted about rooting or software/os modifications.
While I hope to never need warranty work. I feel quite sure that I would get it if needed.
I hate bloatware. managed apps doesnt do a full/complete job of stopping all unnecessary (different for each person) services and apps.
I used the Kingo method with safestrap. So I do have a custom recovery in safestrap.
I use HyperDrive7 rom. still new to HD and there are more options that I could dream about. But the phone is snappier (if thats even possible since the was was awesome under stock.. except for the dozens of apps always running and updating)
I agree with others. To root is personal choice. One I made, and many others have as well. Its our phone. We should and can do with it, what we please.