Well then Atari release Falcon with 16bit 50KHz 8 channel sound and Commodore release Amiga 1200 with Paula from 1984.
The Falcon has still two digital sound channels (stereo) but because it has a DSP to do the software mixing, the number of channels is flexible. There are even trackers that do 32 channels like Ace Tracker, Digital Home Studio, Graoumf Tracker and Megatracker. And because the DSP does the software mixing, playing music does not impact the main CPU.
On ST/STEs, software mixing takes indeed more time than "plain" 4-channel Paula music, but it is also much more flexible. The four Amiga sound channels are strictly divided with 2 left, 2 right and for me the stereo separation is sometimes too much. With software mixing you can pan a sound channel between left and right softening the stereo separation or have effects where a sound moves from one side to the other side. Thus software mixing has its advantages (flexibility) at the cost of CPU time. For the STE there are various MOD players that can play Amiga MOD files at the same or better quality than the Amiga although it indeed cost more CPU time but not so much that it can't done anything else as many demos (and some games like Obsession, StarDust) prove.
It is funny that Amiga programmers used Atari ST techniques (started by Atari ST musician Jochen Hippel with 7-track TFMX player used in for example Turrican and Lethal Xcess) to overcome the limitations of the Amiga sound hardware like more than 4 tracks and stereo panning in OctaMED where the hardware has strict left/right separation. But the 7/8 channel mod players had the same problem as on the STE that it took more CPU time so it was usually only used in title/intro screens and not during game play.
You are right that the Amiga is technically superior to the Atari ST/STE in the sense that its graphics and sound hardware makes effects possible with little CPU time that will take on the ST lots of CPU time. The one advantage the ST has is that it has a slightly faster clock speed.
But you have to remember that the ST, in the first few years was far more affordable than the Amiga. The Amiga was technically superior but at a price which made it too expensive as "16-bit family" home computer for most. Only after the Amiga 500 was released about two years later, the price came down to a level that made it compete as family home computer. But until that time the Atari ST was the most sensible choice because it gave you the most value for your buck. But in 1990 things were indeed different and the Amiga 500 gave you most value for your buck.
So for me both are great machines if you put their price/performance in perspective.