The NES' own sound chip didn't have a sawtooth channel, but some games had an onboard sound chip that added one, like Konami's VRC6: https://www.nesdev.org/wiki/VRC6_audio
Perhaps the real distinguishing factor of Matrix isn't its technology, but its governance. Instead of an extensible, plugin-based approach like XMPP, Matrix has just a single "official" spec that can only be extended by amending the spec itself. IIRC this was one of the motivations behind Matrix's inception.
As to whether one approach is better than the other is left as an exercise to the reader :) But having each approach belong to separate projects allows them to carry on as they see fit, and means they don't have to participate in a zero-sum game.