The honest case for when you don't need a tool like this at all.
I want to be fair here — not every team needs this. If you're a solo developer working on your own project, or a two-person team where you both just know what's going on without needing a board synced in real time, adding a tool is probably overkill. You'll spend more time setting up policy than you save.
Jitly starts paying off once you've got a team big enough that "just remembering" stops working — when people forget to move tickets, when branch names get inconsistent, when standups turn into "let me check git log real quick" moments for everyone.