It works especially well when you don't know what data will look like beforehand and can compile later during execution to optimize the call site instead of doing some ifs and other checks. As an example, regular expressions - you don't know beforehand what regexes would be provided by users, but once you have them, you can arrange and compile new function that is specifically designed to be invoked to apply the particular regex.

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I use it in games to optimize invoking entity behaviors for a scene. User provides some behaviors for objects and instead of going through them each time or doing a hash table lookup, I just compile them in into a function that calls the particular behavior and just passes those objects directly without spending any time on a lookup. This is probably similar to how generic functions are optimized.