I don't think this is a reasonable approach. That's just a way to introduce bloat. Importantly, std does not differ from other crates, except for stability guarantees, so there would be no positive here. All it does is link the library's release cycle to the compiler's. (In fact, rustc-serialize used to be built-in, so Rust tried to go that way.)
But also, serde_json isn't large by default. I'm not sure where you are getting those numbers from. serde_json isn't large, serde isn't large. They both have very low MSRVs few other crates support, so in all truth they can't even have many dependencies.