But I don't think this carries much weight anymore, might have been true way back in the days.
C gives you more control, which means it's possible to go faster if you know exactly what you're doing.
There's nothing special or magic about C code, and, if anything, C has moved further and further away from its "portable assembler" moniker over time. And compilers can emit very similar machine instructions for the same type of algorithm regardless of whether you're writing C, Rust, Go, Zig, etc.
Consider, for example, that clang/LLVM doesn't even really compile C. The C is first translated into LLVM's IR, which is then used to emit machine instructions.
But if you're using it in the sense of "C is a privileged language in terms of its connection to hardware architecture, " well, C isn't, and that statement is patently false. There's not a major difference between C, C++, Rust, Zig--even going as far afield as bytecode languages like Java and C#, or fully interpreted stuff like Python or Perl, especially as far as computer architects are concerned.
(And in the sense of "this is the language that architects care most about for tuning performance," I think that's actually C++, simply because that tends to be the language for the proprietary HPC software that pays the big bucks for compiler support.)
I've never seen a good way to make a CPU that's good for "not C" languages. Those are usually by people who are aggressively uninterested in being fast and so insist on semantics that simply wouldn't get faster if done in hardware. Like the way most Haskell programs execute is just bad and based on bad ideas.
But in both cases, modern CPUs are mostly network- then I/O- then memory-bound. Most C programs aren't written to respect that very well.