It used JMP, but you looked up the API base addresses from a fixed address, ($4 IIRC) so it worked basically the same. But only like some turned based games, and like some chess games etc used that API. The rest maybe used the APIs to allocate a screen but they were banging hardware after that. Most didn't even use the OS even to read the keyboard, which became an annoyance on the A600 which lacked some of the keys.
The original Amiga platform had no MMU, hence no support for memory protection or virtual memory addressing. Some Motorola processors included it (the 68030 and up) but these were only used on high-end Amigas that were not the most common platform, and are more comparable to contemporary workstations. The AmigaOS just used the single address space approach, that's not necessarily incompatible with protected memory.
The Intel 80386 and its successors were quite exceptional in being "killer micros" with a workstation-class feature set for the time.
Memory protection was basically impossible or at least "Research Level Hard" on the Amiga, because of how the OS was designed with linked lists and message passing of pointers. This was what made it so fast, but at a cost. (They would have needed something like Rust to balance that.)
Everything could have been fixed with the March of Moore. The OS could have gotten a hypervisor and been running each program in its own "VM" thinking it was the only program on the machine.
Later iterations of OS extensions on the ST got memory protection support, albeit a bit inconistently and with likely backwards compat problems. FreeMiNT I think supports MMU + protection on 030 machines.
Achilles heel for classic MacOS, too. Sins of our fathers.
Pretty sure MultiTOS (which was derived from MiNT IIRC) fully supported preemptive multitasking back in 1992 or so when it came out. This, plus the fancier graphics support, a proper 68030 instead of the rather cut down 68EC020, and addition of a Motorola 56K DSP, meant the Atari Falcon was superior to the Amiga A1200, at least on paper. I certainly adored mine when I owned it not that long ago as a part of my small collection.
