Do you realise 70% of the atmosphere is nitrogen? We will not run out of it.

make that 78%

Removing the nitrogen bottleneck would let them capture carbon faster. Given our predicament I'd say we should take all the help we get.

Remove too much carbon however and the plants die.

We don't want a Great Decarbonification Event.

Decaying plants emit carbon. The extra nitrogen would just be changing is the length of the give-your-carbon-back-to-the-atmosphere queue. It's negative feedback: stable.

Nitrogen is inert. Even if you could run out of N2 (unlikely), it would have no effect.

Except burning your lungs in the not-so-long run, as they are not evolved to deal with a pure oxygen atmosphere.

Lungs are damaged by high PPO2, not high FO2.

Lungs do absolutely fine in 3 psi pure oxygen.

That's wrong, the fact that is inert doesn't mean it's useless

If you remove all nitrogen from atmosphere, there WILL be consequences

Current planes will not be able to fly since they will lose 70% of lift. They will grow gigantic wings.

There'd be less drag on rockets too. That could be a plus for when we need to escape the death spiral we create

The sibling comment about lift is one of the few things I can think of. Birds would have a tough time.

Eliminating a gas while keeping all other partial pressures constant only affects physical processes. Biochemistry on the other hand only relies on partial pressures, and the number of organisms which interact with atmospheric nitrogen are literally so few that you could count them on one hand.

A photosynthetic organism that fixed more nitrogen than it needed would (1) be at a terrible competitive disadvantage (nitrogen fixation requires a great deal of energy), and (2) would be a source of fixed nitrogen when it died, boosting the growth of other plants that could leech off its efforts.