Any problem with installing two identical circuit breakers in series?
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.