FPGA is a little bit of overkill, but it'll surely work rather easily, especially if you want to generate and mix gazillions of channels.
FPGAs do not have DACs. Logic is pure digital. Thus you'll need to use external DACs. On the other hand, FPGAs are very fast, so you may be able to generate fast PWM and pass it through a low-pass filter to get a decent sound signal.
Also, FPGAs are more expensive, they require multiple voltages, they don't have flash. So making an FPGA board is more difficult than MCU, but you can buy a ready-made one to start from.