Actually weathering can happen on the timescale of decades; it's all a matter of how much surface area of the rock you expose. Nature does this too slowly. In terms of energy input, grinding rocks gets a huge head start with all of the mine tailings we already have. Here is an example:

https://pubs.acs.org/doi/10.1021/acs.est.3c03609#

In terms of capitalism, for me it's not too simple. Capitalism is a profit driven model that can't comprehend long term ecological damage. It becomes a "negative externality" which can then be modelled by economists however they want (which is why they don't agree about how bad it is). If we had a system based on human well being we would have solved climate change already. It's simply not profitable to replace the fossil fuel economy with renewable energy sources. It requires a level of investment capitalists can't comprehend. This is largely why societal change comes from governments which can simply invent money to throw at a problem (think New Deal or Bidenomics).

The complicated part is answering why humans can't seem to get past capitalism. I think we all agree the system is doomed; we just can't figure out how to get away from it.