The SSME low-pressure pumps (both fuel and oxidizer) are mounted to the vehicle structure and don't gimbal. The high-pressure pumps are gimbaling with the engine, so the propellant lines between low-pressure and high-pressure pumps must be flexible. That includes not only the pump discharge ducts (2-3 MPa), but also the turbine inlet (29 MPa) on both low-pressure pumps and turbine discharge (21 MPa) on the LPFTP. This looks a like a lot of articulating joints (3 per flexible line, based on illustration below) on pressurized lines, meaning a lot of potential failure points.
What is the reason behind such engineering decision? Why are the low-pressure pumps not gimbaling with the engine? If they were mounted to the engine, all the lines downstream would be rigid. The flexibility of the propellant lines would be provided by the supply manifold upstream of the low-pressure turbopumps. This looks like a simpler solution, because of:
Lower pressure in these ducts (0.2 - 0.7 MPa)
Lower number of required flexible lines. I am not 100% sure by this, but it seems very likely, because there would be only 1 flexible line upstream of each low-pressure pump (2 for a single engine), instead of 3 downstream of the LPFTP + 2 after the LPOTP (that is 5 for a single engine). Multiply these 3 extra lines by the amount of articulating joints needed on each flexible line and it looks like a significant reduction of critical moving componens. There are of course other flexible lines connecting the engine with the orbiter (fuel tank pressurization, helium inlet, fuel bleed, etc.), but I think their number would be unaffected by the proposed change, so I am not counting them.
There must be some hidden reason why the SSME designers chose to fix the low-pressure turbopumps to the orbiter and forced themselves to use multiple articulating joints on high pressure lines. I would like to understand that reason.