Oh boy.... please don't ask if crickets are good or bad. sparks will fly. the truth is, some people swear by them and some swear against them.
As far as importance of "variety" I'm not sure it really matters. BUT most of us do enjoy watching the variety. Flower mantids love flying insects, so seeing them grab a fly from the air is cool, but looses it's thrill after you see it every day. There is also the idea of sweet treats, bee pollen and honey for example. But I've raised some on one food source to success, so I don't think it matters to their health.