Twitter at its most basic has a product problem and not a revenue or sales problem. I think for product problems founders have a unique perspective and legitimacy to make tough decisions. My guess is that the need for this founder perspective coupled with the fact that Jack was the only founder who was even partially available led to the decision of having him on as part time CEO.
Yeah it's a pretty bad sign for your company when even the founder is like "this kinda sucks, I'm going to a better company that actually makes money."