A question about activer mixer

I am wondering why textbooks tell that the switch transistors operates between cutoff and active region in an active mixer(Gilbert Cell). Since the four switch transistors performs as switches, can they work between cutoff and triode region instead? what is the difference?
I see switch transistors operates between cutoff and triode region in may passive mixer topologies.

Thanks.

Going between full on and full off will maximize the conversion gain. Lesser than this will still work.