But were the software people actually right, or did they just follow the well-trodden path of VMS / UNIX, instead of making full use of the x86 hardware?

Having separate segments for every object is problematic because of pointer size and limited number of selectors, but even 3 segments for code/data/stack would have eliminated many security bugs, especially at the time when there was no page-level NX bit. For single-threaded programs, the data and stack segment could have shared the same address space but with a different limit (and the "expand-down" bit set), so that 32-bit pointers could reach both using DS, while preventing [SS:EBP+x] from accessing anything outside the stack.