It depends on the codebase. If the code base deserves to be a case study in how not to do programming, then a rewrite will definitely yield better results.

I once encountered this situation with C# code written by an undergraduate, rewrote it from scratch in C++ and got a better result. In hindsight, the result would have been even better in C since I spent about 80% of my time fighting with C++ to try to use every language feature possible. I had just graduated from college and my code whole better, did a number of things wrong too (although far fewer to my credit). I look back at it in hindsight and think less is more when it comes to language features.

I actually am currently maintaining that codebase at a health care startup (I left shortly after it was founded and rejoined not that long ago). I am incrementally rewriting it to use a C subset of C++ whenever I need to make a change to it. At some point, I expect to compile it as C and put C++ behind me.

Data structures like maps and vectors from the standard library are still incredibly useful and make a fantastic addition to C if your focus relies on POD types, though if real time performance with heap cohesion is a problem then you’re right to go pure C