To understand why many people say this you first have to understand the android structure...
User installed apps are located in /data/app
System apps are located in /system/app and /system/priv-app
The data partition has its' own alloted space
The system partition also has its' own alloted space aside from the data
Without root the user has no write access to the system partition(fact).
The carrier and oem bloatware that people are always complaining about are usually located in either two locations in the system directory. When removing said apps from the system dir you open up space in the system dir that you cannot use without root and a little hackery(
hackery guide here).
When you install apps normally from the play store they install to data not system. So no matter how little space you have in data or how much you have spare in system that does not change. The system space is not used unless you root and do some hackery.
The real benefit from removing bloat is in reducing ram usage, network data usage, and background resource to reduce or eliminate lag.
Currently I have 17.16gb free in data and 1.76gb free in system. The system space is useless to me since playstore apps will not install there unless I do hackery that I simply don't care for.
One other thing, if you decide to move apps to system when those apps update you will have two copies. When a system app updates from play store, it installs the update to /data/app leaving you with the older copy in system now consuming space on both directories.
As you said this info will be repeated all over this forum and quite frankly all over the internet because it's true.