would have to control for such factors as "governance" when running so-called "growth regressions/barro regressions".

At first the concept of "absolute convergence" came up, i.e. all countries converge to the same "steady state" (the steady state is reached when a country only grows at the constant rate of technological progress ("balanced growth path"), which was assumed to be exogeneous (determined outside the model). I guess Charles Jones, an economist, termed it "manna from heaven"). Then a couple of economist showed up and said something like: Hey, countries may have different structural parameters and they may converge to different "steady states" (for example, if one country has an optimal savings rate and another country has a suboptimal savings rate, then the country with the "dynamically inefficient" savings rate will never catch up to the country with the initially higher income. So, the concept of conditional convergence was born and economists included variables in their growth regressions to control for such differences when calculating the "convergence parameter". The next step was to include variables that proxy for the things you mentioned in your post. If "governance", "trade openness", "quality of institutions", "inflation rate", ... make a difference, then they have to be included in the model... otherwise the model would be misspecified and all those variables would show up in the error term... Actually I don't want to continue writing since I would remind myself that all those growth regressions are trash anyway. ;-D