I like the first principles thinking, but what if they do have a secret place?

What if it goes to the roots and then into fungi and bacteria in the soil or something?

I'm no plant surgeon, but this is correct. Many plants host symbiotic microorganism ecologies in their root system. Usually they help with pre-processing key nutrients (mainly nitrogen) to make it easier for the plant to absorb, and they take a little food out of the roots in return.

By the same token, plants convert carbon into fruit, which animals eat and then metabolize back into CO2. At the end of the day, all of a plant's captured carbon will return to the ecosystem one way or another. Most of the time, anyway.

You could do an experiment where you have a plant in a pot on a scale, weigh how much water you give it, and calculate expected evaporation.

Then, at some point, remove and weigh the plant to see if it contains all of the accumulated mass.

If I recall correctly, other than the last step, that was how someone first noticed that plants must be gaining mass from the air.

At the risk of sounding incredibly ignorant here (which I am) and also apologize in advance for the joking tone for what is a very serious topic...

Couldn't it also be that they can absorb more CO2 when there is more CO2 and that the global rate of absorption is scaling w/ increased CO2?

Maybe plants are gluttonous? Maybe plants will soon be dealing with their own obesity health crisis (that as a side-effect benefits the planet)?

Not sure if this is just a tongue in cheek response, but cellulose isn’t fat, plants use it to give structure and rigidity to their cell walls. Animal cell walls do have lipids, but these fats not responsible for what makes animals obese.

It is also a matter of other related costs likely hydration or thermal reasons. There are adaptations to recycle carbon within rather than the obvious thing and just open their stomas to get more carbon dioxide.

There's a finite limit to how fast photosynthesis reactions can go. You're limited by diffusion of molecules through the chloroplast. Water and CO2 molecules have to bump into the active sites in order to react, and this just takes time.

As well, you'll probably be limited by water transport through the plant. Remember that most of the machinery in a plant is not actively powered. Water is drawn up passively through capillaries. Gases are exchanged through simple diffusion.

I'm sure there's more subtle details about the chemistry that puts an upper bound on reaction rate, but I failed chemistry so I can only speculate.

They're not proposing that plants changed. They're proposing that current frequently used carbon cycle models are off.