At least that’s the message I take from a recent study published in Nature Communications entitled Ecological networks are more sensitive to plant than to animal extinction under climate change.
In particular they found a higher risk of animal co-extinction with plant extinction than vice-versa in mutualist networks. This may be because animals often provide redundant services to plants, and plants have alternative pathways (e.g. self-pollination, parthenogenesis, seed banks, clonality, and/or adult plant longevity) for the reproduction services provided by animals.
While this study used data from Europe in its simulations, the mechanisms invoked should apply to terrestrial ecosystems more generally.