most plants get nitrogen from the air. some fix it from the soil.

Nope, that's backwards. Most plants rely on nitrogen that they obtain
from dissolved nitrogen compounds (NO, ammonia,nitrates, etc.) in the
soil. "Nitrogen-fixing" plants obtain nitrogne from bacteria that fix
it from the atmosphere (by converting N2 to ammonia.)

This is why trying to increase plant biomass usually requires input of
nitrogen fertilizers.

Yes, making other plants nitrogen-fixing would be spiffy, but you also
have to consider something else: Once a plant dies, all the CO2 that
has been sequestered in its tissues goes right back into the atmosphere
through burning, decay, etc.

M. Reed