Why?

I mean, I've got a ZX Spectrum and looking on game protections (and I guess that RNG too) it's easy to see that much of that stuff relies on cycles being accurate (or, at least, R being accurate). If you shorten instructions, the behaviour of R will be different.

OTOH, I don't know about Z80 clones with better instructions per clock. Z80B can run at higher clock speeds, but that's not what you're asking. Russians made a lot of clones based on their own implementation of Z80, but I don't know if that processors are faster. Also, Z80 "cores" have been used on many devices (i.e.: mp3 players) and running at higher speeds (I had read about one of those "cores" running at 25Mhz), and I guess that those "cores" could have faster instructions... but surely they're not available as DIP40 chips.

Zup wrote on 2020-07-02, 18:56:

Why?

Good question. Mainly curiosity, I guess.
Another reason: I've got an old Z80-based TNC (Pk232) that I'm about to repair.
Since it has a very old NMOS version of the Z80 installed, I thought about replacing it by a CMOS version that's less power hungry.
Doing so would make it possible to run it from battery or 13,8v lead accu for a longer time.
And while I thought about this, I wondered if there are modern Z80 wannabes with lower clock cycles.
Of course, I know about assembly code and related timing issues that could occur with non-standard hardware.
I just thought it would be interesting to give it a try nevertheless and see how it goes..

A very quick search leads to the Z180:

https://en.wikipedia.org/wiki/Zilog_Z180

Not sure how compatible it is or if it has any advantages.... And the Z182:

https://en.wikipedia.org/wiki/Z80182

Of course one would need adapter PCBs to get it running in a Z80 socket...

EDIT: looking at the datasheets I am not sure if it is that easy. Might be that they need some other accompanying ICs to do useful work. So probably there are no true drop in replacements...?

MSX TurboR machines have something that sort of fits the bill, no pin compatibility though...

I had issues replacing old NMOS Z80 cpus with newer CMOS ones on my SEGA wonderboy arcade board so keep that in mind - you might go for an upgrade and end up troubleshooting non-existent issues.
I also remember reading something about this for Amstrad CPC systems last year.

It seems that the main difference between NMOS and CMOS variants are:
- Behaviour of bit 3 and 5 of flags.
- A undocumented instruction that behaves as out (c),0 in NMOS variants and as out (c),255 on CMOS variants.

I guess that features are rarely used, but...

Also, I've found some more information about russian clones (mostly the U880). It seems that they recapped or obtained the circuit designs to make a clone... I've only found a difference about flags after OUTI, but nothing more. Nobody mentions nothing about accelerated instructions (and, because of R, it would break compatibility on various spectrum games) nor about pinout differences.

Wikipedia says that Kawasaki has a binary compatible processor (KL5C8400) more efficient than original Z80... but (although it can operate in Z80 compatible bus cycles) I don't know if it allows +5v operation (so an adapter could be easy to make). Also, they mentions the eZ80... but I'm not entirely sure that it is 100% binary compatible.

It's not a direct plug-in replacement, but there was an add-on board for the TRS-80 Model 4 called the XLR8er that connected a sideboard to the CPU socket with a cable: http://www.trs-80.org/xlr8er/
It used a Hitachi HD64180 which is more or less the ancestor of the Z180 (and neither support the Z80's undocumented instructions). Unfortunately the XLR8er seems to be pretty rare and I don't know if anyone's cloned it...