Mostly the `final` keyword serves as a compile-time assertion. The compiler (sometimes linker) is perfectly capable of seeing that a class has no derived classes, but what `final` assures is that if you attempt to derive from such a class, you will raise a compile-time error.
This is similar to how `inline` works in practice -- rather than providing a useful hint to the compiler (though the compiler is free to treat it that way) it provides an assertion that if you do non-inlinable operations (e.g. non-tail recursion) then the compiler can flag that.
All of this is to say that `final` can speed up runtimes -- but it does so by forcing you to organize your code such that the guarantees apply. By using `final` classes, in places where dynamic dispatch can be reduced to static dispatch, you force the developer to not introduce patterns that would prevent static dispatch.