It did become popular because it was decentralized, but the specific features that this enabled were less about not depending on a central server, and more about being able to work with the same repo locally with ease without having to be online for most operations (as was the case with Subversion etc). Git lets me have a complete local copy of the source with all the history, branches etc in it, so anything that doesn't require looking at the issues can be done offline if you did a sync recently.

The other big point was local branches. Before DVCS, the concept of a "local branch" was generally not a thing. But now you could suddenly create a branch for each separate issue and easily switch between them while isolating unrelated changes.