You're right, the dragonflies can't procreate if all their eggs are eaten, but it's not too likely that will happen. Dragonflies breed successfully in water bodies with fish all the time. Some eggs get eaten but some don't. Unless your pond has too many fish, in which case you'd be seeing dead ones, some eggs should survive.
Most California dragonflies oviposit on the surface of the water, which is where Mosquitofish typically feed. Getting them to lay in a wire basket would be challenging, to say the least, and then the nymphs would be trapped there with no food. Damselflies oviposit in plant stems, where the eggs should be safe from fish predation. Once the eggs hatch, the nymphs will settle on the pond bottom and begin hunting. As they get bigger, they might even prey on the young fish!
Don't forget, a healthy ecosystem has all sorts of predator-prey interactions and fosters a lot of death and destruction, which is the foundation of life itself. There's probably room in your pond for dragonflies AND mosquitofish.