Obviously the three check-in's cost more. But there are other costs involved, especially when bags go missing - the cost of a courier to deliver your lost bag will wipe out any saving made by through checking. Then there is the whole back office environment (people and computer systems) you need to maintain to deal with all this.

But I suspect that airlines are trying to reduce the revenue leakage. Except for mixed cash/redemption scenarios, you only buy separate tickets because it is cheaper. I think they rather have you buy the through ticket. And this also makes taking advantage of cheaper fares elsewhere more difficult because you ca no longer through check from your positioning flight all the way to your final destination.

By the way, I am not agreeing or condoning this - just trying to understand their rationale.