This would imply a single/global runtime along with an unrealistic API surface;
For 1) It's common enough to have multiple runtimes in the same process, each setup possibly differently and running independently of each other. Often known as a "thread-per-core" architecture, this is the scheme used in apps focused on high IO perf like nginx, glommio, actix, etc.
For 2) runtime (libasync.so) implementations would have to cover a lot of aspects they may not need (async compute-focused runtimes like bevy don't need timers, priorities, or even IO) and expose a restrictive API (what's a good generic model for a runtime IO interface? something like io_uring, dpdk, or epoll? what about userspace networking as seen in seastar?). A pluggable runtime mainly works when the language has a smaller scope than "systems programming" like Ponylang or Golang.
As a side note; Rust tries to decouple the scheduling of Futures/tasks using its concept of Waker. This enables async implementations which only concern themselves with scheduling like synchronization primitives or basic sequencers/orchestration to be runtime-agnostic.