Not sure I'm convinced.
1. The local airport might be a "greener" way to travel. It is more accessible by transit than Pearson, and is closer to the dense downtown group of origins. People from downtown can take a streetcar to Billy Bishop, or in some cases walk. Even if they take a taxi, it is a 3-5 km drive vs 20-25 km to Pearson. People from outside downtown might take transit to Billy Bishop, while a large majority of those using Pearson either drive or take a taxi.
Furthermore, Billy Bishop's fleet is largely or entirely turborpops, which are more fuel-efficient than jets for short and medium distance trips. And in the near future, if electric aviation advances, the first electric planes are likely to be small planes. There is nothing that prevents small planes from using Pearson, but the fact that Billy Bishop can only handle small planes might give that greener option a competitive advantage.
2. The local airport is kind of a tourist attraction on its own right. Small planes, going over open lake, easy to observe from the coast; that's kind of cool.
Highrises, walkable streets with retail, and parks are staples of the urban fabric, that's all good. But in order to have a city with character, some one-of-a-kind elements are needed, too. Otherwise we could say that CN Tower and Ripley Aquarium aren't needed, either, let's replace them with a condo and a small round park.
3. Billy Bishop wasn't a single-carrier airport. Both Porter and Air Canada were there, I don't remember whether WestJet was.