If you don't bother to use branches (it seems easy enough to pretend they don't exist for this project at least), then what advantage does git have?
The best advantage of git (or another DVCS) is that it is much more fault-tolerant than centralized version control.
A local version of a repository (what you get from a "git clone", the equivalent of an "svn checkout") is the
entire repository. All history, all artifacts, everything. This means that if your central repository takes a dive, everyone who has an up to date clone has a full backup.
Since clones are fully fledged repositories, it also means that you can push code changes from your local repo to someone else's local repo (provide you have network access of course) while you wait for the central repo to come back up. Once the central repo is back up, those changes are pushed to the central repo and everything continues as if nothing happened.
As an example, let's pretend that we were using git on sourceforge rather than SVN. (Also I apologize for picking names and details out of a hat, this is just an illustration)
1) Sourceforge goes down
2) Rather than waiting a week for sourceforge to come back up, Fewyn sets up a new temporary git repo on the kolmafia.us servers. (If Fewyn doesn't have a clone handy, any dev with a clone can basically give Fewyn a fresh clone)
3) matt.chugg updates the build process to point to the temporary repo rather than the sourceforge location.
4) Veracity commits changes for more deck of every card functionality and pushes them to the temporary repo.
5) Lostcalpolydude pulls the changes down from the temp repo, commits the fixes for inline item descriptions, pushes them to the temp repo.
6) Other devs push their own changes to the temp repo.
7) The build process picks these changes up and churns out jars as if nothing is wrong.
8) Sourceforge comes back online
9) Fewyn (or any of the devs with an up to date local repo) push the missing changes to the sourceforge repo
10) matt.chugg updates the build process to point back to the sourceforge repo.
11) The build process picks up changes and makes jars as usual.
Git (or any other DVCS) are built for this kind of thing. They are built to handle any necessary merging in case dev A tries to push to the repo without dev B's code. Their automatic merging is light years ahead of an SVN merge.
To throw my own two cents in (as someone with a professional source code management background but not a script or kolomafia dev and thus little skin in the game) mercurial (hg) is much easier to transition to from an svn background. The git command line has a lot of power but has piles of command line flags and arguments that are really confusing for someone starting out. Mercurial's command line is much closer to SVN's command line and TortoiseHg will be familiar to anyone used to TortoiseSVN. (For some reason, TortoiseGit is not nearly as well developed as TortoiseHg and TortoiseSVN). With that said, mercurial does not have anywhere near the adoption that git does, so online resources for git repo hosting and commands and whatnot are much more prevalent than the mercurial equivalent. Either git or mercurial will be better than SVN, even if no fancy branching is used.
http://hginit.com/00.html is an excellent SVN to mercurial overview written by Joel Spolsky of the Joel on Software/Stack Overflow/FogCreek fame. It is worth reading even if we move to git, as the principles are the same even if the specific command are different.
tl;dr:
The best advantage of git (or any DVCS) over SVN is that it can easily adapt to the loss of a central repository and continue functioning. With SVN, you are dead in the water when the central repo is down. Anyone using git has a fully functional copy of the central repo, which can be turned into a new central repo