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Which distros work like that? (speaking as a Ubuntu user that has never tried any other distros)

Gentoo and Arch are the ones that come immediately to mind. The term to look for is "rolling release".

I think I also read somewhere that Ubuntu is considering a rolling release model in the future.

There were plans for a rolling release called "Grumpy Groundhog", which would exist alongside the stable releases.

Here's an Ubuntu wiki article created by Mark Shuttleworth on it, but note it hasn't been modified since 2008 - https://wiki.ubuntu.com/UbuntuDownUnder/BOFs/GrumpyGroundhog