I have been hearing that even though leaf shutters are relatively expensive, they also last longer than other kind of shutters. Can anyone debunk this?
Interesting question! First of all, it depends on what you're comparing leaf shutters to. I would expect some antique shutter designs like guillotine and rotary to be even more durable.
But I suppose the intended comparison is with focal plane shutters. These have more mass to throw around over larger distances and hence the forces involved should be greater (it's difficult to estimate how much greater, though). If so, I would expect them to be somewhat more likely to fail than leaf shutters. In many focal plane shutters the curtain is also of some kind of cloth, which is relatively easy to damage (e.g. burn a hole in). Finally, leaf shutters tend to be built into the lens and are thus less exposed to the elements.
That is a very generic statement and its validity will be very dependent on which specific shutters are being compared.
If you compare an early in-lens aperture type leaf shutter to an early fabric (silk) focal plane shutter, then yes, the leaf shutter will likely last longer (in both age and actuations).
But if you compare the leaf shutter commonly used in compact mirrorless digital cameras (e.g. my Fuji x20, x100, etc.) it will have a life expectancy more aligned with mid range DSLRs; likely around 150-200k actuations.
That would be better than the life expectancy of some entry level cameras using focal plane shutters rated at 50-100k actuations. But that is not better than the life expectancy ratings of the top line DSLRs using modern carbon fiber and kevlar focal plane shutters, at 400-500k actuations.
The only camera in this database that I know uses a leaf shutter is the Sigma dp1; and its' shutter life is awful compared to other cameras. Not that it means anything specific to the leaf shutter designs (there are many); it just shows that over-generalizations like those statements aren't really useful.