Turns out, this actually happened. 100 years ago, the American Chestnut tree accounted for 25% of all trees in north america. There used to be over 4 billion of them, then 99.9999% were killed by a blight. Today, only a few thousand exist in isolated groves. Few in the US know about this. People go hiking in the Appalachians and think, "Ah, such pristine nature." It is telling that such a profound extinction scarcely registers on any national measurement of health, quality of life, or economic prosperity.
As I said, most of the species we need to survive are domesticated. And most of the others we need are so prevalent and resilient that they'd survive a nuclear apocalypse. Moreover, this problem corrects itself. If a wild species we use becomes scarce (or demand increases), people start growing it. This has happened with paper farms, aquaculture, and even truffles. When it comes to existential risks, lack of biodiversity is not worth worrying about.