Answering my own question. From Wiki article:

> The primary aim of Pleistocene Park is to recreate the mammoth steppe (ancient taiga/tundra grasslands that were widespread in the region during the last ice age). The key concept is that animals, rather than climate, maintained that ecosystem. Reintroducing large herbivores to Siberia would then initiate a positive feedback loop promoting the reestablishment of grassland ecosystems. This argument is the basis for rewilding Pleistocene Park's landscape with megafauna that were previously abundant in the area, as evidenced by the fossil record.

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> Zimov and colleagues argue for a reversed order of environmental change in the mammoth steppe. Humans, with their constantly improving technology, overhunted the large herbivores and led to their extinction and extirpation.[8][9][11][12] Without herbivores grazing and trampling over the land, mosses, shrubs and trees were able to take over and replace the grassland ecosystem.[8][9][11][12] If the grasslands were destroyed because herbivore populations were decimated by human hunting, then "it stands to reason that those landscapes can be reconstituted by the judicious return of appropriate herbivore communities."

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> A secondary aim is to research the climatic effects of the expected changes in the ecosystem. Here the key concept is that some of the effects of the large herbivores, such as eradicating trees and shrubs or trampling snow, will result in a stronger cooling of the ground in the winter, leading to less thawing of permafrost during summer and thereby less emission of greenhouse gases.

The general idea is that ecosystems consisting of grasslands with herds of large herbivores are better than any others at rapidly fixing carbon and building rich soils, significantly more so than forests. The way this works is that grasses have very dense root systems and grow fast, especially when they are being cyclically grazed down to a stub (but not totally removed... goats don't work here because they don't leave enough). The herbivores in turn process that biomass into high-quality fertilizer and spread the micronutrients around by migrating between areas of different soil composition. The result is that the top few meters of soil are filled with a mixture of living and aerobically decaying grass roots, creating relatively stable humic compounds which serve as long-term carbon storage.

There is quite a bit of evidence for that theory... it's not completely uncontroversial, but people who have tried it in practice, i.e. raising cattle by the Voisin method or using Alan Savory's "Holistic Management" or similar approaches, usually swear by it, and theoretically it makes makes enough sense to warrant further investigation.