Is there any reason not to use stereo speaker cable?
"Level" (voltage) isn't likely the issue here — while the voltage can vary much more widely than line level, it is unlikely for the voltage in any modern speaker system to exceed the voltage rating of the wire insulation, and it may not even be particularly higher than line level connections. The difference is in the load impedance (likely 2-8 Ω rather than “high”) and therefore the current (higher). That does mean you're right to want heavier wires, though a regular cable might work fine.

A common source of larger gauge three-conductor cable that comes to mind would be grounded AC line cords. The insulation will be overkill, though (both for the higher voltage and for wear resistance/safety), which will make the cable less flexible and larger diameter than otherwise.

You could make your own cable by using one-and-a-half lengths of standard speaker wire and twisting them tightly together, letting them relax again, then applying braided or spiral cable sleeving along the length, or heat-shrink tubing at key points.

You may also want to reconsider using TS/TRS connectors, as they can short together the contacts if partially unplugged, which might be  worse for a speaker amplifier (originally intended to be entirely internal to the guitar amp, too) than other devices more usually using such connectors which are designed to tolerate the temporary short.

As to why no "stereo speaker cable" exists, it is probably just that left and right speakers are put in separate places so two separate cables are needed, and using a partial run of three-conductor cable would be more complex.