Graphic fidelity on the 16-bit machines was great. Latency was sometimes bad, depending on how much they were trying to do in the game loop.
I can't recall many games with "low responsiveness to joystick movements". On the contrary, latency from movement to action were typically lower than on modern hardware.
It could be that what they wanted to do just couldn't be done in 1 frame. Or often it could, the games were just poorly optimised.
There were plenty of games where the code didn't care to pick up the joystick movements in a reasonable time, making the game feel sluggish, even if the joystick movements can be read directly from the CIA port.
Compare games with perfect framerates like Turrican 2, Superfrog or Leander, with games that don't, like Magic Pockets, Xenon 2, Driller. In fact, compare the official version of Stunt Car Racer with the cracked version, where the crackers massively improved the drawing speed and thus the framerate!
Compare the scrolling of https://youtu.be/V1R7Pd329Bc?t=1969 or https://youtu.be/wFtLGDywZlg?t=553 with https://youtu.be/_4U4ZW37haU?t=114 or https://youtu.be/BXR2yswfC6E?t=862 -- it's purely the programmer's fault.
So in other words it wasn't generally an issue with the Amiga, but with sloppy work.
> There were plenty of games where the code didn't care to pick up the joystick movements in a reasonable time, making the game feel sluggish, even if the joystick movements can be read directly from the CIA port.
We clearly had very different experiences. To me that is not something that every concerned me.
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.