Most of the 8-bit microprocessors I'm aware of -- including the Z80 and 6800 -- only had single-bit shift/rotate instructions, which didn't require a barrel shifter. Variable shift instructions were comparatively rare.
Besides, a 32-bit barrel shifter is considerably more complex than an 8-bit one. It's not just four times larger to deal with the wider operands; it also needs another two levels of muxes, making it closer to 6x as complex.
> most of the 8-bit microprocessors only had single-bit shift/rotate instructions
Yes, they don't have a barrel shifter because they don't have variable shift instructions. But unfortunately, you didn't answer the actual question: Why didn't they have it then? As I've already asked, Was it technical/cost limitations? Or was it simply the lack of demand/commercial reasons to add one?
Besides, a 32-bit barrel shifter is considerably more complex than an 8-bit one. It's not just four times larger to deal with the wider operands; it also needs another two levels of muxes, making it closer to 6x as complex.