I don't think this is nearly as bad as the grandparent suggested though. The language is young, I'd prefer experimental features remain in the experimental branch rather than get bad design stuck in the language.
I think if you're doing dev, it's completely reasonable to expect the dev to install a newer toolchain. Cargo makes all of the actually painful parts of contributing to a project pretty trivial.
On another front, Rust is working hard to get people off of nightly. This project, for example, uses 3 unstable features. Clippy can already work on stable (edit: code that is linted with Clippy can also build on stable in some setups), Custom Derive will be stable in less than a month, and inclusive ranges is a pretty minor feature.
I would expect this project to begin working on stable for Rust 1.15, but I'm not affiliated with it directly, that's just my guess.
No. But we plan to make it work.
In any case, the nightly split is Rust deciding that it is good to allow people to use experimental features (i.e. working out if they're good/bug free) while also resisting infecting code that doesn't want to risk breakage---such projects use a stable compiler meaning even their dependencies won't be able to accidentally rely on something unstable---and thus hopefully avoiding defacto stabilisation of low quality features.
[0]: https://blog.rust-lang.org/2016/05/13/rustup.html