Zig and Jai were designed to not require the C runtime library. You can't replace C if you're building on top of it, can you?
You'll need something to set up an entry point, stack, somewhere for assert() failures to go, etc. The C library is minimal enough and fine for that. If you know what you're doing, it's easy enough to take care of those services yourself with DasBetterC.
That something can be written in machine code or the alternative language though. Could you provide a link for DasBetterC? Googling didn't really lead to anything.
The name is a bit of a pun. I wrote a presentation at DConf "D as Better C" and noticed what I'd unintentionally written :-)