System users often don't have a real home directory, but need somewhere to write files too.
Yes, system users tend to not have a home directory. But you are fully able to create one for a new system user if this is what you want to do.
You are also able to create all kinds of temporary directories and read-only filesystems for a process (e.g. using systemd) if this is what you want do to.
Yes there is a lot of fragmentation and no real standard, which is a little disappointing, but you sure have options to work with. And these options do not have to involve any legacy-ish filesystem components like /var/tmp that nobody knows the purpose of.
The purpose of /var/tmp is temporary files that should survive a reboot. A potential example where that would make since is a partial download file. It is only needed temporarily but if a reboot happens while the download is in progress, you probably don't want to have to start over.
Also if /tmp is or might be a tmpfs, it is probably desirable to use /var/tmp for larger temporary files that don't fit in RAM.