What would happen if the stamens are removed from the flowers?

"All insects, birds, and land animals (even us) would cease to exist."

Incorrect. Flowers weren't around untill 125 millions years ago, making them 300 million years younger than the oldest plants.

If flowering plants were to go extinct, non-flowering plants would fill in the niche left by the extinct flowering plants. This would go accompanied by a animal mass-extinction event, caused by the disappearance of the flowering plants that formed a substantial part of the food chain.

Short answer: A mass-extinction would follow if flowering plants go extinct. If they never existed, the animal kingdom would never have adapted to flowering plants to begin with.