I'm not going to argue with TI, it's their chip . However in practice this isn't an issue for complete amps or amps using typical modules. Take two Fosi V3 monoblocks, it doesn't matter if they share a DC power supply (shared 10A) or an AC power supply (2x5A). Each amp has its own internal power supply (PVDD) reservoir caps. The TI app note is more relevant for amps with common supply _after_ the PVDD caps. Which may be an issue for you in your compact DIY build but not for these Fosi amps or any others using modules with separate reservoir caps for each chip.
Power supply pumping is a concern but usually handled by wiring each module in alternate senses at input and output, so module A has inputs and outputs wired as normal, while module B has input signals inverted, and speaker outputs also inverted, for the same result but opposite power draw. Once that is dealt with the clock sync question is mostly moot I think, especially for music signals.
Back to the main point though, there is no downside to having a shared 10A supply instead of two 5A supplies for the Fosi amps.
And if your main speakers have a HPF (generally 80hz or something like that) ... the power current requirements are ridiculous, I mean, the PSUs will be laughing all the time.