Question: Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit.

What if I install two identical breakers sequentially (one after another) so that if one of them fails the other one steps in and disconnects the circuit? Is there any problem with such installation?

Answer: 
There is no problem here.

In fact, this is often how subpanels are configured; the main panel has a breaker that feeds the subpanel, and the subpanel has individual circuits protected with their own breakers. The subpanel will have an amp rating. The minimum of the subpanel rating and the ampacity rating of the wire feeding the subpanel will dictate the appropriate breaker for the main panel.

Appliances that require their own local disconnects (such as air conditioners, water heaters, etc.) frequently use a small enclosure with space for just one circuit breaker. This could be a good option for whatever application you are thinking of.
Most generator manual transfer switch-over panels require you to do just this. The wire coming out of the breaker and going to a load (normally) is disconnected and channeled over to a second panel with another breaker and then then the biter-end coming out of the second panel is tied back to the load. In short, two breakers in series.