But BIND isn't just failing because "it's written in C", it's failing because it's written in terrible C. That said, "terrible C" is probably most every C routine written by someone with less than 10 years of solid low level experience, so "writing good C code" is not very scalable. There are active, solid projects with very few security exploits that are written entirely in C. Nginx comes to mind.
The article makes a brief reference to DJBDNS, which is written in C, but has suffered zero security exploits [1], and is extremely performant. And it is being used in production, so presumably if it had any exploits they would have been exposed by now.
But...DJB's code is (usually?) released under a rather unfriendly (though mostly open) license, and DJBDNS hasn't been updated in some time, so a more modern project isn't a bad idea. And Rust developers can probably write solid code with only a few years of programming experience, which makes it easier to extend without adding security holes on a weekly basis (coughBINDcoughOPENSSLcough)...