No, because an ALU instructions with a register as source is already running as fast as possible (at 4 clock cycles, which is the duration of an opcode fetch 'machine cycle'). Or from a different perspective: an 8-bit ALU wouldn't have made math instructions faster, but would have cost twice as many transistors.
The 4-bit ALU is just an internal implementation detail that isn't visible to the outside (except maybe through the existence of the half-carry flag which indicated a carry from the lower into the higher nibble).
And if you want a CPU replacement that plugs directly into old home computers, the CPU needs to have the original instruction timing, otherwise software that depends on 'cycle counting' won't work (probably less of an issue on the ZX Spectrum though because the Speccy didn't have a programmable video hardware like for instance the Amstrad CPC).
The eZ80 is a modernised and more efficient design, with (among other things) a wider ALU: https://en.wikipedia.org/wiki/Zilog_eZ80. Not an option for keeping old home computers alive though, for this you'd want an exact Z80 clone with the original timings and undocumented behaviour.
Managed to produce a program where with key presses, you could change delay in the loop in +/- 1 clockcycle increments. Mind you: fastest Z80 opcodes take 4 cycles.
How then? Well, there's also opcodes that take 5 cycles. Or 6. Or 7. And 8=2*4, 9=4+5, etc. Program just automated the insertion/removal of those in the inner loop. Of course I had to pick instructions that didn't mess with some Z80 registers.
Great fun (& educational) figuring out stuff like that. Fun times...
I pretty much knew all the clock cycle counts for the instructions as a teenager, and you would code assembler with them always in mind.
Ah clever! Didn't think of that. Probably the closest thing to "racing the beam" since the Atari 2600 :)