I guess the reason being that the plants would convert all the CO2 to O2 in the greenhouse and then suffocate without the vent or pumped CO2.
Is that the most economical way to keep the greenhouse warm enough?
There are heat exchangers which are passive devices you can attached to an intake and exhaust to reclaim heat.
Burning gas in the enclosed space not only enriches the CO2, but also warms up the greenhouse even more.
" The supply of extra carbon dioxide is an often applied method to increase the yield of greenhouse crops."
So I'm not sure what your point is.
In an open atmosphere plants aren't limited by available CO2, they are limited by sunlight, temperature, soil nutrients, or usually water availability. Adding more CO2 has little to no benefit for the plants.
It turns out the answer is Yes – in a big way. A new study published in the April 6 edition of the journal Nature concludes that as emissions of carbon dioxide from burning fossil fuels have increased since the start of the 20th century, plants around the world are utilizing 30 percent more carbon dioxide (CO2), spurring plant growth." - https://www.noaa.gov/news/study-global-plant-growth-surging-...
1000 cubic meters of air only has something like 150 grams of carbon in it; even if your plants in question are 95% water, you're still only talking a few kilograms of plant growth before you completely exhaust the air in an enclosed space.