/mnt came first. and distros started mounting stuff into it. but actually it was never meant to be used for that. it was supposed to be an always empty directory where a sysadmin could mount something temporarily if they needed it.
so distros moved away from /mnt and started using /media
then /run was invented as a place for all that semi-automatic temporary stuff that needs a place while the system is running.
by looking at where a distro mounts stuff, you can see how long they have not bothered to follow changing standards.
personally i wish /media would have stuck. i find the current paths /run/media/username/device rather unpractical. whenever i connect a data device i have to go searching for the mountpoint.
giving sensible defaults to automatic mounts is the issue here.