Can a Z80 be powered at 3.3v and still run reliably at 3-4MHz?
The datasheet says Vcc= 5 V &plusmn;5%.
At the time the Z80 was introduced 3.3V logic was completely uncommon (if not non-existent).

Cf. this table about different logic families, typical supply voltages and year of introduction. 

The Z80 dates back to the time when TTL-LS (low-power-Schottky) was common.