It's both. Programmers' visions for their games either had to be scaled back because the 68000 just wasn't fast enough, or they implemented what they wanted and it tanked the framerate. Sometimes they met in the middle because the programmers thought 25/30Hz was good enough. Sometimes even the finest programmers, with the most optimised code, ended up with a 25Hz game because what they wanted the game to be demanded it.
Of course, some programmers said "this entire game has to run in 1 frame" and made of sure that. Sometimes it's the same programmers, e.g. Sensible Soccer is typically 1 frame, but Cannon Fodder is often not. Uridium 2 is typically 1 frame but Fire & Ice is often not.
The Amiga 1200 opened up new games possibilities, not just because of its added bitplanes allowing 256 colours, but also because having 2MB of Chip RAM instead of 512KB, and a CPU roughly double the speed, made more games viable.
> We clearly had very different experiences
It will depend on the games you played. Something you can try as a challenge: complete the first level of Magic Pockets on an unmodified Amiga 500 (or an emulation of one at its normal speed). Feel how laggy and awkward it is. Even a video doesn't give you that understanding. Then try the first level of Superfrog.