I'm not going to fault this piece for being hand-wavy and poorly justified: it is that, but then again, it's a piece of popular journalism which is allowed to be. So, I'll criticize the broader idea.

This article cites China as a model. Hong Kong did not pull the rest of China up as it grew. It certainly played a role, but frankly the communism that took resources from the urban coast and built roads, schools, and other infrastructure in rural areas was more likely a bigger contributor to the massive improvement in (purely economic) standard-of-living for most Chinese.

It was in particular /not/ enlightened foreign rule of urban areas that did this. If we accept that all geopolitical entities respond to incentives, it is not clear that direct foreign control of areas of the developing world will produce the ideal outcome for those areas: this will only be the case when the incentives and interests of both the local population (which is not monolithic, btw, but we'll ignore that for now) and the foreigners align; long term prosperity requires that incentives align for both in the long term, which seems terribly unlikely. Moreover, the history of development is fraught with stories stories good-intentioned outsiders failing to make a beneficial impact because they poorly understood the complex local situation, and it's simply unrealistic to assume you can just start with a clean-slate-by-fiat in a "charter city" and build without considering a place's history.

I think Romer has a good core idea, one that few people would argue with. Namely, development is not just a matter of fixing the "Production = F(capital & labor)" equation; good governance, good ideas, and good people all are required. While it may be surprising to some, this is an idea that is pretty well understood (at least at a high level) in the development community/industry. My beef with his idea is a flawed execution, and one that I think could be potentially damaging in the long term. These ideas need to come from local populations and make sense for their own contexts.

As an analogy, you just aren't going to reproduce Silicon Valley by emulating the Bay Area's regulations and investment level: there is a whole history that made it the way it is. Attempts to do so are kind of doomed from the start, so it's better to focus on creating new centers of prosperity that make sense for the local context. I don't think foreigners are well positioned to do that.

---

Another point to make, the Millennium Villages Project had a similar premise to Romer's. The idea was that solving the problems of poverty in particular villages through strong international partnerships would lead to spillover effects throughout the surrounding areas. Everything I've heard about it is that the results have been alright, but not really that great. Besides a bit more of a heavy-handed foreign-involvement approach, I'm not sure if the "charter cities" idea really is that different than MVP and hence it's not clear how it will overcome the obstacles MVP faced.

Edit: William Easterly is quoted here. He has an awesome book, "The Elusive Quest for Growth", that discusses a lot of non-intuitive reasons why development efforts have historically failed. I would highly recommend it.