Just because expert C programmers were able to make it work doesn't mean that C is the best way to write secure code. I say this as someone who writes quite a bit of C (though I don't view myself an expert in it yet).
So, a combo of top talent w/ a C history and tons of tooling made most of them go with C. Many others went with Ada/SPARK. A few small fish even use typed or structured assembler. C is only chosen due to tooling and "better the devil you know" philosophy. Work on superior languages got more results with less effort in both human and mechanical reviews, though. So, the inferior language is only used due to an accident of history.
Details on that here:
Those are the recommendations in that order. What you use depends on your domain, constraints, skills, and so on. Modula-2, Active Oberon, Modula-3, Free Pascal, and Component Pascal were probably closest to C's domain in terms of safe, efficient, easy-to-compile languages. Ada is systematic in all the errors it handles but with steep, learning curve. SPARK straight up proves your code. One can also use DSL's/4GL's that generate proper C w/ automated checks like iMatix and Galois do (and I once did). I've also seen Ocaml and LISP used for real-time, even embedded, systems with custom runtime. Ocaml was also used for tooling w/ source to object code verification.
So, there's a number of options. Each are behind C currently in tooling due to limited uptake and investment. More uptake and investment can fix that. Even so, average results of those tools have far lower defects than C code with shorter time to train people (ignoring Ada). That most teams aren't composed of geniuses in safe coding means that's important too.
These more mathematical languages have to prove themselves out with real-world examples, algorithms and compiled code, before I recommend them. I'd like to see CompSci keep hammering away at them to find easier and easier ways of learning and using them. Not to mention improve tooling.
1. Be closer to English to make them easier to read. Important as software is read more than written. Also can help in reviews.
2. Generally have proper features like modules or interfaces to aid programming in the large.
3. Still efficient enough for programming close to the metal.
4. Prefer sane defaults or automated checks on issues that trip programmers up. A good implementation usually lets you turn these off for a module if needed.
5. Tradition of thorough language reports and grammars means less undefined behavior.
6. Most common stuff is still efficient once compiled. If Wirth-like, then also efficient to compile.
7. Less tied to a specific processor style with its own style being more amenable to safe, maintainable operation. See Burroughs B5000 processor vs PDP-11's.
8. IMPORTANT. Easier to develop tooling for verification, esp static or dynamic analysis.
9. Easier to verify mathematically.
So, these are some things off the top of my head that various languages more ALGOL-like did better than C-like languages. I wouldn't say there was a single one that had all these traits but Modula-3 came close. A modified version of Go might as well given its predecessors were used in safe-language OS's. Hope this brainstorm gives you some idea of what things I valued vs C's style.