Here's the thing, a good 35mm image will look better than a good APS one but the same could be said for 6x6 Vs 35mm. 35mm has a problem though, poor 35mm images don't come out at all! So many images are lost because the film was put in wrong and didn't advance or the camera back was opened half way through fogging the photos and lastly my personal favourite putting the same film in the camera twice. So many lost photos and family memories. APS avoids all of this, so a good or even poor APS photo will outshine any of the millions of lost 35mm photos. Sure if you are a keen or pro photographer 35mm or 6x6 (or bigger even) is the way to go. But for someone's family snaps APS was way more reliable.
Then there were technical advantages. APS records exposure data on a magnetic track on the edge which the printing machine can use to better match the printing exposure. It was also possible to pre order extra prints when you took a photo (sadly this was mostly turned off a few days after the first APS went through the lab as users wouldn't read the instructions and inadvertently order 99 reprints of every frame and got quite cross when presented with a d and p bill of £300 or similar).
Talking of reprints, enlargements etc the negatives (or slides) came back safely in the film cassette with an index print (like a miniature contact print) which was cross referenced to the cassette with easy to see images and frame numbers. What's not to like with that?
Kodak, who largely invented it, caused a lot of the negative publicity by makeing a million models of crapulent plastic cameras and rushing to sell product before the infrastructure and their fellow APS manufacturers were in place to Handel it.
Speaking of cassette formats being more reliable than 35mm why did 126 die out? You have all the same safe handling and reliability of a cassette format with a larger film format quality (28mm square against 24mm on 35mm in the vertical format. Plus it's square which just looks better and avoids having to choose and latter display a mix of portrait and landscape images).
APS came out just as home pc computers were starting to become a thing. There was a lot of innovation in APS like a photo player to show your Holliday snaps to all your neighbors on a TV set at the same time instead of passing around prints. There was a film scanner as well but it was all too late. Digital was just on the horizon and arrived before a new film format could get established. Had it arrived 10 years earlier it could have made it.