The “Hegemon style charter city” seems limited to colony relationships. I am proposing a guarantor style charter city:

While my model has not to my knowledge been tried, it seems like a viable economic model, and it is not clear Romer proposed this, however unless there is an enforceable long term hands off agreement, investors would be naive to invest:

1. The hegemon gets replaced by a guarantor.
2. The guarantor is not a colonizer, rather there is a contractual relationship where a formerly unreliable partner (nation) is buying reliability.
3. The charter city is expected to generate high profits, that get taxed at a moderate rate. The host nation and the guarantor share this tax revenue. The guarantor shares its legal system, and collects an insurance premium for enforcing the rules governing interactions between charter city and host country.
4. The host country benefits from foreign and domestic investment in the charter city, something that previously would not happen, because of a history of nationalization of businesses.
5. Furthermore, economic activity in host country beyond the charter city might increase from supplying the charter city with physical goods, utilities and/or services.

This seems like a win/win, and if colonialism/hegemon charter cities is like rape, then this guarantor charter city is like prostitution, something non religious libertarians defend.

The key is that an international framework that effectively punish the guarantor as well as host country if they try to exploit businesses or population of charter city beyond the terms of the charter. For this to work, guarantors need to be regional powers weaker than USA, Russia or China, and recognized as more reliable than the host country.