I don't think the theory holds merit.
1. Because I'm not convinced that Columbus is struggling to revitalize. This is an assumption. I am not convinced that Columbus is in worse shape than other cities of comparable size and amenities. All cities have gone through a period of losing population, and issues with urban revitalization... if this were only happening in Columbus, then I would look for a local rationale.
2. I think one of the absolute strengths of the local economy is the relative diversity of the city's job base, spread out among government, private, and education sectors.
3. Government jobs, while perhaps not as high paying as some private industry jobs, tend to be more stable. You typically do not see massive layoffs of government employees. Stability in unemployment ultimately helps economic growth.
I think you need to look at the unique geographic and historical development of Columbus to find solutions to this issue. While it is far more complex than what I am about to summarize, here are some of my thoughts.
Columbus has PLENTY of dining and shopping options, as this website shows everyday; however, a significant majority of them exist in the suburban areas. Columbus is very much a city driven by annexation and suburbanization; therefore, the density of the dining and shopping options are more spead out, as is the population. Shopping and dining are not concentrated beause neither is the population. The population isn't concentrated because the city grows through annexation and suburbanization. If growth boundaries were established here, as they have been in, say, Portland, I think you would quickly find that growth pressure would direct inward once again. There are no geographic boundaries that prevent Columbus from sprawling ever outward, which is why the core is diffusing. While public policy may help re-create a core, I really doubt that, lacking any real geographic boundaries (as in Manhattan) or created boundaries (as in Portland) we will see a return to pre-suburbanization densities, densities that support shopping and dining variety.