There are not many application domains left where the performance difference between C#/Java/BlitzMax and C or C++ really matters (where C++ programs usually already perform slower than C programs).
True, but the main "domain" where the performance difference does matter happens to be the games programming domain.
But in all honesty - when do you really need more performance than today's Java, C# or BlitzMax already give you?
You need maximum performance...
1. When you're programming a game you want to run on older hardware
2. When you need fast A* algorithms, collision detection, raytracing, and practically any other game-related task
3. When you don't want to be stuck at some point of the development of your game because a certain technique you wanted to implement just won't work fast enough
Etc.
Not all parts of an application usually require the highest possible performance, but those parts that do still can be written in C and linked to the remaining application.
That sounds like a good method, if it's possible. I don't know much about JIT, but isn't it impossible to use unmanaged code from a managed program?