Posting a kid song maybe explains why your point of «CO2 is plant food» is oversimplified. That is only a small part of the truth and misses the full picture of how our climate system works.
Discussion
Charlatans hide behind complexity, confusion, and “trust the experts”.
I will give you the benefit of the doubt to simply explain your objection that;
1. CO2 is not plant food
2. CO2 is not plant fertilizer
I think the correct way to look at this is bottlenecks.
Does more CO2 actually help plants in a statistically detectable manner, or is there something else preventing it from going faster? (such as a hard limit on how much photosynthesis can happen, or not enough sunlight)
Unequivocally yes
Has it been proven under equal environments (excl. CO2 ppm) with different plant types and a somewhat large sample size?
My objection is about your conclusion, not the two points you mention.