Being differentiable does not make something a neural network nor does it mean the differentiated function is meaningful (such as can be the case in highly branching or otherwise complex control flow). It also doesn't always escape combinatorial explosion and that fixed structure limited precision strictly bounds how far a neural net could look ahead.
By making something differentiable, you're hoping relaxations or some smooth proxy doesn't break fundamental structure, allowing you to solve an easier problem than discrete combinatorial search. Sometimes there can be barely any leveragable structure. This has proved very difficult to achieve in general and is a sort of holy grail in some fields.
That said, there are powerful game playing AIs that use either no (DeepNash) or minimal (DORA) search. But in general you can't get something for free, you're always paying something with an approximation.
By making something differentiable, you're hoping relaxations or some smooth proxy doesn't break fundamental structure, allowing you to solve an easier problem than discrete combinatorial search. Sometimes there can be barely any leveragable structure. This has proved very difficult to achieve in general and is a sort of holy grail in some fields.
That said, there are powerful game playing AIs that use either no (DeepNash) or minimal (DORA) search. But in general you can't get something for free, you're always paying something with an approximation.