Within 300 million years life may not even be able to exist on land, and by 1 billion years the oceans will be evaporating [0]. So the timeline you have given for depletion of bioavailable carbon is already muted by unavoidable solar expansion. Do you have a source for a shorter timeline?

> Lack of biodiversity in the short term is a much smaller problem in comparision

Where do you think coal comes from? That carbon was sequestered during the "Carboniferous" period---a time when the trophic web lacked the diversity of organisms capable of recycling carbon in the form of cellulose. Biodiversity is the reason carbon can be reprocessed and keep circulating. A major simplification in the trophic web is precisely what allows carbon to stop cycling and become trapped in sinks. The fewer organisms in a trophic web, the more likely dead organisms will sink into anaerobic reservoirs before being recycled.

Similarly, Snowball Earth: a case of high biomass and low biodiversity. Nearly all life on earth went extinct because of a lack of organisms capable of offsetting the byproducts of other organisms.

> Useful nitrogen is not scarce compared to useful carbon.

The opposite is true, which is why you will see nitrogen fertilizer and not carbon fertilizer. Inorganic nitrogen is common but is energetically expensive to fix into organic compounds. Nitrogen fixing organisms are at the base of the trophic web and they limit the biological productivity of ecosystems.

> Similarly, earth is made up of 80% iron. We're not running out of it either.

It is not evenly distributed. There are vast areas of ocean whose productivity is limited by the scarcity of iron available [1]. This is seen in ocean blooms caused by iron oxide transported from the Sahara by wind. This in turn causes atmospheric carbon to circulate into the ocean through the formation of diatomaceous matter.

[0] https://image.gsfc.nasa.gov/poetry/venus/q79.html

[1] https://link.springer.com/chapter/10.1007%2F978-1-4899-0762-...