I'll bite. Our CAR ran over a small nail and had a slow leak that we had to keep pumping up. We did that for kind of a long time until the pumping became daily. All the tires were near the end of their tread life but otherwise OK. The car is AWD so the tires last a very long time. They also need to be replaced in matching sets of four to minimize excessive differential wear. All that factored into our decision making, but on Black Friday I found a deal and purchased 4 new tires.

So, sometimes it might make sense to live with certain leaks for awhile. But not on a bike! Not only is the problem cheap and easy to correct, but a logical person would assume that a leaking tire is more likely to leave you stranded than a good one.