O Alpine Linux é projetado exatamente da maneira que você descreve. O texto a seguir (de minha autoria) é em seu wiki :
Another distinctive part of Alpine is its variety of "installation
modes." It can be installed to a hard disk/SSD/other storage medium
like any other distro; this is called the sys mode. The storage medium
in question can be removable, if you like, so long as you can
configure your machine to boot from it. However, if you're working
with removable media, there are two other installation modes you might
consider. In each of these modes, you will boot your machine from a
static ISO image (either a CD or a USB partition configured like the
CD). You will also need a writable medium to save updates to the
system. In the diskless mode, this writable medium is typically a
small USB key (or a second USB partition) that holds the changes you
want to persist. Both the base Alpine system and all your changes will
be unpacked into a memory-based filesystem. The other, data mode is
for cases where you're dealing with a large amount of persisting data,
that you want to keep on a hard disk/SSD/other storage medium, rather
than unpacking into memory. The default setup here is to store your
/var partition directly on the hard storage medium. But as in the
diskless mode, your root system still comes from a static ISO image.
The second and third modes are sometimes referred to, collectively, as
"run-from-RAM" installations.
Key to the second and third modes is Alpine's lbu utility. This tracks
which files you've modified from their static ISO version, and want
the changes to persist. The lbu utility saves those changes in .apkovl
"overlay" files (these are essentially tar-gzip archives, though they
can also be encrypted).
You can use the lbu utility with the sys mode, too, if you like: as a
form of backup, or to configure overlay files for other systems. But
for a robust incremental backup system, you'll probably want a more
specialized tool.
O que você está visualizando é o descrito acima como o modo "sem disco". Você pode configurar a lista do que é persistido e o que não é feito da maneira mais detalhada que você desejar. Além disso, você pode configurar para que as alterações sejam persistidas apenas quando você solicitá-lo explicitamente.