I think it usually gets down to the fact that if the implementor views him or herself as a capable C programmer, he/she is going to want to implement in CVI rather than LabView. As mentioned, the granularity is there to be more certain you can implement a solution, even though you may write a whole lot of code to do it rather than connecting icons with lines.
If the workload is such that non-programmers have to do a lot of development, I'd say CVI is not the answer. With C, the paradigm is "trust the programmer" not to do stupid things, and non-pro folks can't be trusted not to do genuinely stupid things in C. They may well be intelligent professionals in their field, but that doesn't make them capable programmers. Some of the most botched up code I've ever seen was done by system engineers / EE's who had read the first three chapters of K & R and declared themselves C programmers. Poor programmers, and with no grasp of even the simplest design concepts, they hack out gobs of code that typically breaks at runtime because they've mishandled pointers/arrays. But most of these can eventually learn to accept advice as to how to structure their code.
Worse are those who have taken a couple of programming courses at the local junior college and weasel their way onto projects and strive to make themselves indespensible. Too stupid to be embarassed, they are unable to accept any guidance as to style or form. I find they often form up into a "conspiracy of fools" to cover their mistakes, or ingratiate themselves with a scientist or engineer who can't code at all.
I can't tell you how many times I've had the seniormost technical professional involved (usually an engineering fellow, tech director, or senior scientist) come to me to help unhose bungled CVI applications, often after the culprits shoved aside my participation in the first place.
On the other hand, the point to most systems isn't to have good code or a good software design. The domain knowledge involved is almost always going to be held by non-software people. Many want a sense of "doing something" as a day to day activity - and they often gravitate to coding if they can at all do this. A pure C programmer isn't very useful, generally speaking - you have to work in some domain.
Of course, NI knows all of this, that's why they have both products.
Several groups I know of are now doing test SW impementations in C# and Visual Studio - sure, it's Microsoft proprietary, but intellegent non-software people are better able to implement using OO (and avoiding pointers and memory management). I think NI's done what it can to approach the whole .NET thing. But they didn't even try to accomodate Java, which I would have liked to have seen.
There are several threads on the website in re CVI Vs. LV.