"The initial motive for rooting is normally to install a custom rom".

Nope.

Rooting has nothing whatsoever to do with installing a custom rom.

Root is a function within a rom - it's the equivalent of granting admin access in Windows (root means you have write access to the root directory). Most ROMs that you can install aren't rooted themselves. That's how little root is related to rom.

What is common between rooting and a custom rom is the requirement for an unlocked bootloader.

I've rooted almost every phone I've owned (since 2009), and all but the last 2 never had a custom rom available. Most phones don't have a custom rom available - it's a rare phone that does have a custom rom available.

Check out rom developers, like Lineage, to see how many devices get custom rom support.

You don't necessarily need to root to install a custom ROM

On a Fairphone at least you can practically flash the device OOTB after unlocking the bootloader, no root needed.

I have never met a person that just rooted their phone without slapping a custom ROM on it.

Now you have

The initial motive for rooting is normally to install a custom ROM

I think there are some misunderstandings.

Root is not needed to flash a custom ROM. That does not (usually) happen from a running system, but through fastboot or the recovery, and those don't ask for root permission, only an unlocked bootloader.

It is OS endorsed by Xiaomi. Plus I've paid for the device, so it is up to me what I do with it.

Is there a way to lock the bootloader and keep a ROM different from the one the device shipped with? Or do I need to relock and reunlock every time I need to update the custom ROM, with all the data loss this implies?