Mappy is using a softsynth technique. The ARM CPU in the cart is running the synth algorithm, and it passes sample playback values to the 6507, which has to update TIA with them every single scanline, even when the screen is not being displayed.
Stella's Stocking is doing something similar without the ARM chip, but due to the lack of hardware assistance, it can only play music during the title screen.
The 7800 could do this too, but it would tie the hands of the 6502, and we'd still be requiring an extra (much more difficult to solder) ARM chip on cart, or be stuck with no free time to do anything interesting during playback.
Since the 7800 has an audio pin on the cartridge port (unlike the 2600) it's better to just use an independent sound chip, and not tie the hands of the 6502. Or use techniques that make TIA sound more in tune.