I know I can create a nandroid backup through system settings
No, you can't. Read the tag wiki of nandroid to clear your concept about nandroid backup, including how it is made.
I mostly just want to be able reinstall Android OS or reset to factory default in case my device breaks.
A factory reset wouldn't help since it only clears data, internal SD card and cache partitions while rooting mainly affects system partition. System partition is what contains the files needed for Android to run.
You can use the answers available to Full Backup of non-rooted devices. On a non-rooted device, those answers are more or less limited to the extent of the magic adb can perform. In essence, they would, when possible, copy an app's apk and its data. Some of them covers both system and user-installed apps.
Tip: If an app doesn't want to be backed up (such as Chrome), none of the answers there would be able to backup that app's private data - sad reality of our times.
As for re-installation and possible nandroid backup, the situation differs for device to device. Following are few generic things I can tell:
Your device is popular enough in developer community that at least one person has created and publicly hosted a custom recovery for your device and also hosted the stock ROM somewhere, either by themselves or by making a copy of what OEM probably provided . If there exists a way to flash the ROM without booting into a custom recovery mode, then you can take the moderate risk of rooting.
Make sure you meet all the requisites to flash the ROM before you begin rooting.
Your device's OEM provides stock ROMs image which can be flashed from stock recovery or through fastboot (or equivalent) mode.
Fulfill the requisites of ROM flashing and you can take the moderate risk of rooting.
You own a device with chipset from Mediatek and that chipset is supported by Smart Phone (SP) Flash Tool. If yes, then make the scatter file and use it in SP Flash Tool to make image of your device's partitions. You can call it the true nandroid backup. That backup can be used to restore the Android OS.
Note: If you've a custom recovery for your device, then you can use SP Flash Tool to flash the recovery without bothering to root the device at first. Once the custom recovery is installed and device is booted into, rooting would be a piece of cake.
Make sure you meet all the requisites before you begin rooting.
If there is no OEM or developer support for your device, then I suggest you don't take the risk of rooting. The ending might take away your peace of mind.