Zilog did bring out a range of low-end MCUs, Z86 series
Those were Z8, not Z80, so they had no chance of winning the Z80-user market.
[AVR] are not without warts.
Only three pointer register pairs
Three pointers, four pairs for use with ADIW/SBIW instructions, and all 32 for MOVW. Not all AVRs, BTW.
weird register that must always be 0 -- except when a mul just overwrote it
A compiler convention, not architecture. avr-gcc chose R1 before there was a multiply instruction, which was a mistake. (RISC-V does something similar - An "always 0" register, right? Although that IS at the ISA level, and doesn't have any weird exceptions.)
limitations on registers for many instructions
Mostly, the "immediate operand" instructions only work on the upper 16 registers (of 32 total.)
And the weird (newer) instructions like SPM, MUL, etc.
different instructions to access data in flash (fixed on the latest ones I think?)
only "fixed" on new chips with 48k or less of flash.