Natural processes can include earthquakes, volcanoes, viruses. Its often random. Plenty of reason to think these species have something to offer in the present day.

I think of it like publishing an old book, or seeing an old movie. It is being a good steward of a legacy in a sense.

Also, there are a lot of species that went extinct because they encountered a predator they couldn't deal with - people. Is that a "natural process" just because it happened before recorded history?

I would say that it is a "natural process", we came from nature, and are still part of nature.

Came here to say this, the woolly mammoth, woolly rhinoceros and cave bear likely all are early victims of competition with humans.

"Natural processes can include earthquakes, volcanoes, viruses. "

And asteroids. The dinosaurs got screwed because they hadn't yet developed a space program.

The leading candidate for this extinction was the introduction of humans equipped with bows and arrows into its environment through the Bering land bridge.

The African versions of big species were able to co-evolve along with humans as we developed spears, fire, etc. The American ones did not. This is why the American versions of everything from horses to cheetahs disappeared.

In this case, the animal was in Siberia, not in the Americas. Same theory may apply, though.

We might have had a hand in the "natural process" (which doesn't make it unnatural).

Bring them back I say.

Paging Dr. Malcom...

Hum, nope, ecosystem restauration is not a perverse or silly goal. Species have coevolved for millions of years to make the best, stronger and more resilient ecosystem possible.

But then by restoring the ecosystem to be similar to your conception of a prior state aren't you preventing the continued maturation of that ecosystem, effectively stopping the system from evolving further?

Not. First of all is not our "conception" of a previous state. We know that Europe had a big mammal fauna in the past and that this fauna was erradicated.

Second, We are restoring the coevolution and making the system stronger in fact. A well managed predator benefit to thousands, maybe hundreds of species. Entire communities of insects and fungi need the temporary ecosystems created by predators. Preys benefit also by mean of disease control.

I used the word conception because the view of a past ecosystem is always going to be missing details. Predator prey interactions are chaotic in simplified systems. If there's an insect that affected a plant then herbivorous prey of a mammalian predator can be impacted in ways that can alter the entire system causing an imbalance that has not been allowed for. It is a conception because it is not the previous state you're returning to. For example human occupation levels of some regions are reduced by malaria and bilharzia.

Attempts to introduce species that we thought we understood well have turned decidedly sour in the past, introducing species we know relatively nothing about is unlikely to go well.

You are mixing several concepts here.

Attempts to introduce species have turned decidedly sour in the past... if introducted in ecosystems where they do not belong. Reintroducting a locally extinct species is a different case.

Big felines are very well known animals. Present in all zoos of the world and reproducted in captivity since many years ago. There are entire books published about big feline surgery for example.

It is a conception because it is not the previous state you're returning to.

This is a false problem. The goal is not to achieve a theorical ideal previous state, is to restaurate a missing node to be able to reach a range of valid stable states. Is the same difference as "to reconnect a route bombed in 1940 to drive from a to b" or "to try to frozen the area in 1940". Nobody is talking about to living in caves again and working three hours each day.

If there's an insect that affected a plant... causing an imbalance that has not been allowed for.

All imbalances are "allowed" in fact, there is not a nature police, but your imbalance will never occur. Hervibores will just start eating other species of plants or migrate and quit the area followed by predators until the plant species recover. Mature ecosystems are buffered and can deal with known changes.