TL;DR:
The Z80 was introduced not long after the 8080 and replaced it quickly and almost entirely for personal computing. Still, a large chunk of new software written stayed with 8080 code, making no or only very limited use of Z80 instructions.
Are there any reliable numbers of the amount of Z80-only software for OS that supported both CPUs? For the fine print see below.
Story Behind
While the 8080 started its CPU lineage in 1975, it was dethroned two years later by the less expensive and (hardware wise) more versatile Z80. Right in time for the home computer era starting ca. 1977. Except for some very early systems (Altair/SOL), late (DAI) or undead (Interact) designs and regional circumstances (COMECON countries *1) the Z80 ruled the market for 8080-compatible CPUs (*2).
Still, even throughout all of the 1980s many software packages did not use Z80 instructions - or in case of compilers, did not generate Z80 Code (*3). There were programs explicitly Z80-based, like ZCPR replacing CP/M's shell CCP with a Z80 optimized version, but it felt like a minority (*4).
This is even more astonishing as not only new computers were designed around the Z80, but also a good part of all S100 systems were upgraded (*5) with new, more powerful (and less power consuming) Z80. After all, early Z80 cards doubled the speed to 4 MHz (*5). Later Cards not only cranked that up to 6 or 8 MHz but offered addressing past 64 KiB, interfaces and even full 64 KiB on board.
Fine Print
What I'm looking for are (somewhat) reliable numbers to get a picture how true my impression is - or not. Of course a relevant result can only be found for operating systems that supported 8080 as well - at least at some point. Main candidate might be CP/M and its derivatives. It does not make any sense to look at OS that were only used with/made for Z80-only-systems, like Tandy TRS-80, CPC or MSX (*7).
A good answer might include some quantification, like how much of a certain software archive is 8080 code vs. Z80 (or later) code. Might be interesting to see what metrics can be used.
Since more software was produced later (i.e. Software production increases a lot during the 1980s), a result might be biased toward Z80, but that's fine as it simply shows at the end of the Z80 era.
*1 - And even here the Z80 was a strong opponent, as Eastern Germany did, unlike most COMECON countries not clone the 8080, but went right away (and 4 years late) for the Z80
*2 - Intel's 8085 did find some usage in portable devices like the Kyotronic series due its low power CMOS version.
*3 - Including Turbo-Pascal. While it and its products needed a Z80 to run, the compiler itself produced clean 8080 code. Only its runtime/libraries contained Z80 code - most likely as they were written in Assembly.
*4 - IIRC, later ZCPR came as well in a 8080 code only version. But my memory might be false.
*5 - All the Altairs and IMSAIs I have came with Z80 cards instead of the original 8080 board. Quite often the Godbout/CopmuPro Z-CPU or the Ithaca Z-80.
*6 - Especially Godbout's Z-CPU was famous for being stable at 6 MHz and above.
*7 - Thinking of it, it might be even more interesting if similar patterns would show up at such systems, as they provide no inzentive to avoid Z80 code. Lets make it an addition for bonus points :))