You nailed it: From day 2 or so we imagined to develop Genode as the future common API for the diverse range of microkernels and showcased the approach with all L4 kernels we could get our hands on. The vision is still to provide a replacement for POSIX in the microkernel world ;-)
Regarding POSIX, we don't think that tools and applications developed for this interface do not fit the microkernel world but on the traditional systems level POSIX (and its tools) is not sufficient to make the best of out of the microkernel advantages. For example, we run libcurl, GPG, libarchive, and coreutils in an orchestrated scenario to implement a robust and secure deployment/installation subsystem in the Genode-based Sculpt OS https://genode.org/documentation/articles/sculpt-19-07.