They cannot do this, unless they create a home directory skeleton template, which would not apply to existing users, and would not do anything to applications installed after the user creation. Additionally, if applications are sandboxed, they won’t have access to the user’s Templates directory anyway. In any case, Linux distributions have abundantly made clear over the past 10+ years that they are not interested in this.
Applications will want to install their own templates, and system administrators will want that too; this means a more complex layout, for instance the one used by systemd for service files:
/usr/share/xdg/templates— distro/app packaging/etc/xdg/templates— site customisation$HOME/Templates— user customisation
In any case, this would require a standardisation effort to ensure that applications can find those templates; right now, they only have one directory to check, which means they’d need additional API and logic to go through all the additional template directories.