Just days before winning the race for speaker of the House last week, Representative Mike Johnson of Louisiana sent a letter to colleagues laying out a plan to complete the budget process by bringing 12 individual appropriations bills to the floor. Mr. Johnson billed his plan as a way to “allow us to demonstrate good governance.”

It put him firmly in the camp of the G.O.P. rebels — like Matt Gaetz of Florida — who led the revolt against Speaker Kevin McCarthy and have been called “whack jobs” by their own colleagues. They have been likened to “economic terrorists” for their actions during budget negotiations.”

But in one way, the whack jobs have a point: The federal budget process is broken, and it’s been broken for decades. What the Republican rebels say they want isn’t congressional chaos, but the opposite: good government, legislative transparency and real democratic accountability when it comes to the power of the purse.

They want to achieve this through a return to “regular order,” which, broadly speaking, means passing individual appropriations bills and allowing for a more open debate and amendment process on those bills as called for in the 1974 law that created the modern budget process.

That is what Mr. Johnson has promised, and indeed the House would be better off under regular order. The biggest challenge in achieving that goal will probably be Mr. Johnson’s ability to manage the G.O.P. rebels who support it but also have consistently undermined it by with attention-seeking maneuvers like shutting down the government or jettisoning a speaker for keeping the government open.

Mr. Johnson is not the first to promise a return to regular order. At the end of 2015, Speaker Paul Ryan declared, “In 2016, we will make it our goal to pass all 12 appropriation bills through regular order.”