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"automated" is the issue when producing chips. You can automate some to a certain level of nm. Have you seen the labor needed for maintaing a single modern ASML machine? Also we got a lot, but Japan has the tools to verify results.
Amiga 1200 is in the ballpark of Atari TT/Falcon and yes STing for IP, browsers etc. were available. But ST was same year as Amiga 1000 which also had just MC68000 without MMU, both Commodore engineers (who designed... Atari ST) and Atari engineers (who designed in HiToro Lorreline - than then became Amiga) had own external MMU.
The Amiga's problem was expensive monitor, flickering screen and... with such great video chip - the default color palette was just abnomination. I know it was made for TV, but that was the problem!
Well, plain ol' Prince of Persia looked much better on ST - if you compare PC/Amiga ports. Look at the torch animation.
Well, that's the HW. As with video, the 16-bits went on further than just mere hardware limits.
When we talk software mixing, STE maxed out CPU at 8 channels 50kHz, here's an example: http://yerzmyey.i-demo.pl/YERZMYEY-Octopush_ATARI_STe.mp3
Even plain 520 ST can do a lot on this YM chip.
Amiga 500 on the other had could a bit of this but only with 12kHz samples, and no volume control per channel, also those pesky filters.
Amiga 1200/4000 could do same - as per much faster CPU, but... they still left the old audio 8-bit chip in it :/
Well, that was the problem. Atari had the MIDI (pro music) and DTP from the start. The mono 640x400 monitor - ultra sharp was a great gig.
Amiga went the road of being console turned computer, and the expansions only created havok with support. Even A500 Plus had issues.
Sadly - it also affects community - the IP rights for Amiga are mess, the recent issue with Terrible Fire extensions - for some reason a lot of bad blood in a very bold and interesting system made by Atari engineers.
Well, I'd argue about the music. The chiptune music from SID and YM has aged very well, while Amiga sounds horrbile without FM synth and 8-bit 11kHz samples.
Also memory was much better organized than Amiga - without the speed penalty.
And the simplicity of Shifter (the "GPU") allowed for really awsome 'beyond the dream' hacks, which were unavaliable on Amiga due to much more capable - but limited in 'hacking' video chip.
And then the first upgrade - Atari STE - amazes today with full control 8-channel 50kHz MODs... While mc68k CPU stayed at 8MHz!