>ugly mess

That may be the case, but there are plenty of examples of elegant implementations.

JUCE, for instance:

    #include <juce_core/juce_core.h>

    class MyComponent {
    public:
        void doAsyncOperation(std::function<void(int)> callback) {
            // Simulate async work
            juce::MessageManager::callAsync([callback]() {
                callback(42); // Call the functor with result
            });
        }
    };

    // Usage
    MyComponent comp;
    comp.doAsyncOperation([](int result) {
        juce::Logger::writeToLog("Callback received with: " + juce::String(result));
    });

.. I think that's kind of clean and readable, but ymmv, I guess?