Your comment reminds me of the sorry tale of Montreal's Mirabel Airport, which opened up in 1975, for international flights, while Dorval was limited to domestic and transborder traffic. Your abovementioned scenario happened almost exactly as you said in Montreal over the years.

Mirabel's biggest problem was its distance from the city centre (some 40 miles). Connecting domestic flights would have required something like 3 to 3.5 hours to connect. A planned rail link and additional highways (which would have mitigated the distance issue) were never implemented due to lack of funds and some political wragling. It quickly became known as a white elephant, and passenger traffic never exceeded 3 million per year (its planned max capacity was 50 million). In time, much international traffic to Canada switched to Toronto---various reasons such as the loosening of the Canadian requirement that Montreal be the gateway for transatlantic flights, economic flight stemming from the rise of pro-separatist sentiments, as well as the inconvenience, have been cited.

Eventually, all passenger traffic was switched back to Dorval (24 km from city centre), while Mirabel only handled some charter, and then, only cargo flights. I heard Mirabel is now slated to be developed as an amusement park!