Natural history DNA is subject to statistical analysis. This analysis can provide insight into previous environments and the adaptations needed to survive them. Humans may have a future use for a solution already encoded by another species.

Biologists have DNA samples of every known species.

Undiscovered potential Most models would place a non-negligible value upon an unknown self-replicating organism that has been adapted to the modelers environment after several million generations. At the very least, identification, classification, and understanding would be attempted before placing a value.

Ok, but how much value would it place on an organism which wasn't adapted to the modelers environment, as demonstrated by the fact that it was selected against and went extinct?

Protection from disease When there are a variety of species, a single pathogen is less likely able to ravage an ecosystem.

OK, but what reason, other than status quo bias, is there to prefer one result over the other?

Protecting minority humans A species of negligible value to a dominant society may be of critical value to a marginal society.

If so, then protecting that species is in the interests of the human population in question, and it then becomes of question of how best to serve their human interests. But that doesn't get you anywhere as far as biodiversity, in and of itself, having instrumental value.

Value from scarcity Economics. As supply decreases, cost increases.

You probably mean price, not cost... but what does that have to do with anything? We're trying to establish that biodiversity has a utilitarian purpose... how does this address that? If something is useless, who cares how much supply of it there is, or how it's priced?

Ethics Treat others as you would have yourself be treated. Don't afflict others with the negative consequences of your actions. Protect the oppressed. Be a good neighbor. Share. Improve your environment for the next visitor. Because you may be judged by the rules you apply to others.

This is just begging the question

Protection of sentient species Some endangered species are capable of learning language. Some humans are not. I typically value worth on a combination of mental traits. Some animals are capable of holding jobs. Some humans are not. Many people often value worth by productivity. Some animals are more valuable than some humans.

I agree that non human sentient species deserve protection, both because their existence has utility (in understanding the phenomenon of intelligence), and because I consider the protection of sentient life to be a terminal value. But what does that have to do with "biodiversity"?