There is a benefit to keeping the rules as simple as possible. Capping the number of flights is simpler to understand. Most of the problems with flying are fairly well correlated with number of flights.

Trying to directly cap emissions seems like a good way to make the program fail before it even starts. Do you penalize fliers who end up on an older, less efficient jet? Takeoffs burn a lot of fuel so do you penalize fliers who take flights with a layover? If a plane flies half-full, do the passengers pay more?