Getting rid of the airport would be a mistake, in my opinion. The biggest cities, nowadays, need two or more airports. One handles international and the most important destinations. The other handles more local service. Look at New York City; it has two major airports (JFK and EWR), and several smaller airports with lots of commercial traffic (LaGuardia, which has international flights; Islip; Westchester County; and even Stewart in Newburgh if you want to count that). Washington DC has Dulles, Reagan, and BWI. Los Angeles has LAX, Burbank, Orange County, Ontario, etc.
Putting all of the flights at Pearson would probably be bad because then the local connections would disappear. Billy Bishop Airport serves flights to places like Sault Ste. Marie, Thunder Bay, Windsor, Ottawa, etc. Airfare is cheaper because there's less demand for flights from Billy Bishop. If you put those flights at Pearson, prices will go up because of the demand for runway space, not necessarily because of more customers. Then flights to other places in Ontario will become less frequent. And when Pearson has to cut flights because it gets too busy, which flights do you think will be cut from service: the flights to Sault Ste. Marie and Thunder Bay, or the flights to Heathrow, Rome, or Los Angeles? Obviously, the international flights will stay, and the people of Ontario will lose a way to move about their own province.
To me, speaking from experience (even I have used Billy Bishop Airport), the airport has value both as a connection at a low cost to consumers to move around central and eastern Canada, and also as convenient access to Downtown for those living in the area, or for charter flights.