They could have used 16 bit segments with no overlap. It would have a 16 bit offset register + a 16 bit segment selector register with the top 12 bits reserved (always 0). 16 bit software would run as usual in a single segment, while larger programs would use both registers for 20 bit addresses.
286 could then use the next 4 bits from the segment register to allow 16 MB address space and 386 could use all of them for 4GB. And wouldn't it be nice if 386 had 64KB pages (1 segment)?
I kinda wish they had. 64k windows with no overlap would make segment registers a slightly inconvenient 32-bit address register.
I get why hey didn't. Someone might want to run two processes each with its own segment, but the whole machine might only have 64k in total.
That wouldn't have worked, the point was to pack data in memory. Even on 64kb computers, MS-DOS 1.x loaded .COM files at the bottom of available memory and allowed using the "familiar" CALL 5 interface even if the program was not loaded at physical address 0x100 (which is part of the interrupt table on x86). MS-DOS 2.x augmented that with TSR (terminate and stay resident) programs that could relocate themselves to use the minimal amount of memory at 16-byte offsets.
The 68000 was a complete break so it opted for relocatable code (which also needed more registers, and in fact the 68k had 16 instead of 8).