Recycling what?

Let's say you have oxygen from somewhere. You use the oxygen to burn hydrocarbons, to make energy and water and CO2.

To turn that into a closed cycle, you need to regenerate the water and CO2 into oxygen, to burn more hydrocarbons. The only way to do that is to add energy - on earth, we use solar energy via photosynthesis, but in space, you could use solar or nuclear energy via some chemical process.

But if you have the energy to regenerate the oxygen, why not just use it? Why make oxygen and then burn the hydrocarbons?

And why bother burning more hydrocarbons when a by-product of the regeneration process is carbon, a perfect fuel!