Why would cells need to break down old mitochondria?

Cells need to break down old mitochondria because they have passed their usefulness. A cell has limited space and resources because they are extremely tiny. So, when mitochondria are no longer able to efficiently produce energy, they have to be removed so that the cell can have its space back and its resources to produce more energy.
The cell will cannibalize the mitochondria and use the atoms and constituent parts to repair damage it has experienced or to build new cellular structures. Cells are incredibly efficient; if they weren't, it would be a lot more difficult for complex life to arise from them. Because of this, they need to be able to recycle and reuse as much as they can. Breaking down and reprocessing mitochondria allows them to create new structures as well as clear out areas in the cell that clog up transport, take up useable area, and burden the cell in terms of energy expenditure.