VPNs prevent your origin ISP from keeping logs; you may not want your office, school, coffee shop, city wifi, etc. to know which services you're accessing.
You can (should) still require identification on your home hosted services, you can log that.
Self hosting would essentially just be using a ramdisk. If you want to be crazy about it, you could even run a VM with its storage entirely within a ramdisk.
Note that the lack of logging probably doesn't matter when your self-hosting, since it's all for you.
Concept of RAM only Linux images with validation and signing is something seen in some datacenters. For example, Lenovo has this in their confluent cluster management (https://hpc.lenovo.com/). A node can network boot or boot from usb (read-only) and all writes go to RAM.
Alternatively, booting a LiveCD amounts to the same thing without requiring a boot server, you have a local 'disk' but nothing writes to it. If extra paranoid you could actually boot it from a burned DVD, but in practice even when booting from USB most 'live' images only write filesystem to RAM.