I would say that os-prober is required to be on ONE system of those present - IF you wish grub to have control of the choice of which system to boot. It serves no other purpose of which I am aware.
If there are multiple systems, each of which is using os-prober to set up its own grub, then there can be difficulties created in the process - as not every system uses the os-prober information in the same way. For instance, many ‘other’ distros do not correctly set up grub to correctly start an Arch-based system - and other such quirks.
Having just one instance of os-prober is one way of avoiding these problems, especially if it is a ‘smarter’ version such as is supplied with EndeavourOS. It can also stop the game of ‘musical chairs’ as to which distro has boot control - as only one will even know that the other distros are present.
All of this is so regardless of whether the system is UEFI based or not. Personally, I always disable os-prober (won’t need to now!), and call grub separately IF required for its handling of special cases such as decryption, or perhaps providing access to snaphots as might be found on a btrfs-based setup. Otherwise I direct boot (in the same manner as systemd boot works, but with rEFInd) without making use of the grub at all.