And yet the SS strain gauge does not require extra wires, I believe. Presumably the light in that cartridge receives its power through the two ground cables? Why didn't DS choose to do that
That is exactly what DS Audio does in all its contemporary cartridges - it uses the two ground wires to deliver DC power to the active LEDs and optical sensors.
A consequence is that there is only one wire left to carry the signal for each channel, whereas balanced operation requires two. So their contemporary 2-channel cartridges do not support balanced operation.
Hypothetically, if DS Audio felt balanced operation was desirable in the future, some other wiring scheme would be needed for 2-channel operation.
They have just released mono versions of their entire contemporary range of cartridges, and these could in theory use 2 wires for the signal and be balanced.
To be clear, all contemporary DS Audio cartridges use the standard 4-wire scheme used in tone arms. There is absolutely no need to rewire.
I plan to rewire my 55-year-old SME arm for entirely different reasons. The primary one is because there is some corrosion around the connectors, and I had to solder one back on. At the same time I can eliminate two sets of connections in the phono path. On the other hand, when something is working, don't fix it!

