I think this is a bit contrived. It's a long way from C to modern web development, but I see no reason why to skip extensive C# experience applying for a Java shop etc.
Or even experience with a different paradigm (such as functional programming). Having worked with a multitude of technologies is beneficial for a programmer. It enhances one's understanding of the craft. It also proves the programmer has flexed their "learning muscles" a lot, which again is an advantage in its own right, since learning is a job never done. Even if you have the just right experience right now, what happens in 3 years?
Of course directly relevant experience should be given clear priority over "other stuff", but I wouldn't be so harsh as to say it better be skipped altogether.