A would-be competitor, in a country not respecting intellectual property laws, might get a few customers by launching our product and charging only a fraction of what we charge. However, what will this competitor do when their customers request new features or report bugs? Obviously, we'd be a lot more nimble in responding to such requests, so maybe this shouldn't be such a big concern after all.
Also, if this does becomes a problem, we can just stop releasing new versions publicly, at which point the competitor's offering would stagnate, while our offering would continue to improve.
No. Worst case scenario is that the competitor has more resources than you and can be even more nimble at adding new features and fixing bugs. Because you made all the source code available, you lost all the 'head start' you had against such a competitor.
Also, if this does becomes a problem, we can just stop releasing new versions publicly, at which point the competitor's offering would stagnate, while our offering would continue to improve.