I was under the impression that nitrogen fixation was still the limiting factor in plant growth. If that's the case, will improving photosynthesis really improve yields?
Yes, it will. Plants need nitrogen to make proteins, and the most abundant protein in plants is RuBisCO - the one that fixes CO2 in the air into carbohydrates to store the energy from sunlight.
Most plants have to produce a vast amount of RuBisCO to make up for the fact that photosynthesis is so inefficient. By making it more efficient, we reduce the amount of RuBisCO needed and therefore reduce the nitrogen required.
C4 plants are much more nitrogen efficient than C3 plants.
I'm a vast gaping maw of ignorance here, but I thought we had solved nitrogen fixation with the fritz-Haber process at the cost of using fossil fuels. Am I wrong, or are we just trying to keep farmers from having to buy ammonium nitrate?
Supplementing nitrogen comes with a whole host of environmental trade-offs. In particular there are problems with pollution, where nitrogen added to fields gets washed off in the rain and ends up in waterways. There it can totally destabilise ecosystems by introducing a flood of nitrogen which is usually a scarce resource, leading to massive population explosions of some kinds of organisms, which in turn can leave huge buildups of toxic byproducts. This is called eutrophication.
What I've been told is that, while fertilizers obviously help a lot, they aren't a panacea and the plant still needs to do some expensive nitrogen chemistry which will set limits to its growth, regardless of how much energy it gets from photosynthesis.
