From mostly an outsiders' perspective, I just don't think C is a very nice programming language. It looks easy to to pick up and it probably is (for some definitions of "pick up"), but I don't think that's a good thing. The language gives you almost nothing. Pointers, structs, arrays, control flow. Not much else. I'm barely exaggerating when I say that all the C code I see looks like a chaotic pointer juggle fest for precisely that reason. The few features and library that it does have come with non-obvious gotchas that will punish you later.
Rust is probably much harder to "pick up", and way more complicated in general, but it's just, uh, more language. I'll take pattern matching, encouraging immutability, functional style programming, trait programming over C's simplicity any day of the week. The safety is extremely nice, but I think Rust's biggest eye-opener for me is that all these "higher level" features are just possible at (close to) the performance of C. That makes it very appealing to me.