It's not clear to me why libcore is problematic in your eyes. It's clear you'd like to use Rust without using libcore, but so far I haven't seen the motivation for why that's worth pursuing.
For C and C++ it's more understandable: the C and C++ standard libraries interact with the operating system in certain ways. But Rust's libcore doesn't really have that problem.
It's not clear to my why this is such a big deal. Stable Rust inherently excludes unstable features. Enabling unstable features is the opposite of using stable Rust.
The one slightly compelling argument I've heard for something like this is in the Mechanism for beta testing unstable features thread. But even there I think the focus is on limiting what unstable features can be used, not necessarily whether stable/beta/nightly channels are used.
As a C/C++/etc. programmer, I strongly disagree. Nightly Rust isn't some #YOLO wild west. It's quite stable (in terms of predictable and correct behavior).