Lots of badly written flash content would (even on desktop) completely peg a CPU core. And it would do that even when the content wasn't visible (for background tabs, or if you'd scrolled past the ad).

This is bad enough on desktop, worse on a laptop (where you care more about battery and thermals) but it was a disaster on the very low power phones we had at the time. It made the iphone's browser feel extremely janky and unresponsive, and your phone would warm up in your hand. People had no idea that the problem was that "punch the monkey" banner ad they had already scrolled past. The website operator didn't know what ads were being served. Everyone just had a bad time.

Steve Jobs was asked about it in an interview once and he said he'd never seen flash managing to work smoothly on a mobile device. He said if Adobe could show it working well, he'd reconsider. But as far as I could tell, Adobe never rose to the challenge. I think android had flash working for awhile, but they eventually dropped it too. (Probably for the same reason.)

On desktop, I remember having an option in chrome to make flash not play by default. That way flash banner ads just wouldn't get loaded. I imagine they could have done the same for mobile safari - but that sort of thing was never Apple's aesthetic.