Jet engines mix the incoming air in a flow that feeds into the burning and compression for thrust. This loses efficiency quickly as you go past Mach2. Rockets use a combustion chamber that is sealed off and has a steady and controlled inflow of oxidiser that is mixed in an injector plate.

They are two very different processes. The additional weight to have different engines means you do not gain in terms of mass.

Super complex systems that can burn both ways are on drawing boards. And have been on drawing boards for 70s years.