I also noticed that 3.1.1 is available on ubuntu snap. At this point I am not sure if I should go with snap or appimage. Either way, it is great to get packages directly from the developers!
Chrome has its own deb repository -- maybe more active projects need this too. (Maybe there's a service to be had hosting and configuring repos?)
I'm on Xubuntu 16.4 and I have 2.9.7 installed. I missed the entire year of developments. 16.10 has 2.9.11 released Feb 4th. 17.4 has 3.1.1 but won't be released for ~4 months. Maybe we should blame Ubuntu for 6 month release cycles, or me for not upgrading, but regardless of the cause, Krita users don't have the new version.
16.04 and onward can now have apps decoupled from the OS release for apps that provide snaps, like Krita does. `snap install krita` will get you 3.1.1.
Worked on 16.10 and I'll use this on 16.4 too.
Distributions put a lot of work into making sure that software they package is managed and handled in a way that their users like. Your example, Debian, is a distribution that favours stability above all else -- so is it a surprise that features are not merged into packages that often? There are many distributions (openSUSE Tumbleweed, Antegros, Arch Linux) that are far more rolling release and have newer packages.
If you want new software, use a distribution that gives you what you want. Don't blame the distribution for providing what the majority of its users (and community) want.
$ snap find krita
Name Version Developer Notes Summary
krita 3.1.1 krita - Krita: the free digital painting studio
For the record, the latest apt version on ubuntu is 2.9.7
BUT most of their work is lost to us due to the way distros handle external software. If you install Krita, gimp, darktable in debian you will get really ancient versions (unless you use a PPA from a mostly unknown source, but even then you can get quite old versions).