You can with systemd (*cue boos from the audience*), although it involves a bit of additional configuration - what files to clean up, and set up a timer.
Wow, thank you! I didn't know it not only exists but is provided by systemd. I'm already using systemd to deploy my services, so this sounds like a perfect fit!
See e.g. https://www.putorius.net/systemd-tmpfiles.html#user-specific... (no affiliation with the site, it was just the first one I found that describes the works).