This is wrong. The Fed doesn’t want higher unemployment. It isn’t even willing to tolerate it. That’s the whole “soft landing” conversation, and why hikes are so hesitant.
The ideal path would be labor market loosening with no more unemployment. Absent structural adjustments, that’s possible. But we need structural adjustments, so layoffs are necessary, which makes the closest to ideal layoffs and immediate reuptake, i.e. constant employment with less wage growth.
A single-mandate Fed would respond to last year’s inflation like Russia did: a sharp, steep rate hike.