GEMDOS / TOS from start have support for Accessories.
Accessories are programs that are available from main application so TOS from start could run few !
If it had been anywhere near real multitasking, it would have been multitasking.
Sound more like the cooperative "multitasking" seen in some versions of 68k MacOS and just like MacOS at that time TOS was heading for a deadend.
Sure solutions could be found, but they allways were compromises between performance, reliability and compability.
AmigaOS3.x on the other hand was pretty much state of the art when it came to consumer OSes and could hold it's water against Win3.x and only got left behind a few years later.
None of the 3 multitasking OSes you mentioned were available/fully useable at the time the Falcon was released.