This is against current consensus. The consensus is that plants do grow faster when you put fertilizer in the soil and the yield increase is because of that, not because of the "grass years".
There are plenty of studies on this, one example:
> Crop yields were increased by 19–41% (rice) and 61–76% (rapeseed) during the two years of rice-rapeseed rotation under NPK fertilization compared to PK fertilization across the study sites. Yield responses to fertilization were ranked NPK > NP > NK > PK, illustrating that N deficiency was the most limiting condition in a rice-rapeseed rotation, followed by P and K deficiencies.
https://www.nature.com/articles/s41598-017-01412-0
Anyway, you are making my point. Notice how you say that crop rotation, soil quality are extremely important. So much for CO2.