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.