Earlier quoted context omitted.
SeL4 is a very interesting kernel even without taking the proof into account (eg in platforms/builds that the proof doesn't cover). I wish someone would build a beyond-posix desktop OS on top of it...
Why is it interesting?
The memory management, scheduling and IPC are implemented in an interesting and novel way (compared to your typical mainstream OS) and allow for quite different OS design.
In particular, capability-based IPC and memory management could provide a robust base for a secure OS from the ground up, instead playing whackamole in an aging POSIXish design.
Sadly (tho I understand the rationale), most approaches to building a full OS on top of (L4 in general) are "run userspace Linux in an isolated container", which kind of ignores all the power underneath.