I wonder why couldn't Intel simply introduce single 'offset' register for apps ported from 8080, and make all other registers 20-24bit. Why bother with 4 different registers and all that segmentation nightmare?
Very few benefits to a clunky 24 or 20 bit word size; now it costs more and is a bizarre boutique architecture in a world where it needs to compete with 8 bit Z80s and 6502s.
The segment register solution does both almost for free in most cases. Code gets a segment, data gets a segment, stack gets a segment... and you are free to use all of memory if you bother to use the ES register. In many cases, that could be isolated to a small piece of the program so that was also quite cheap.
As someone who wrote code in assembler, Pascal, and C for those machines: it wasn't at all a nightmare. It was quite easy and simple.