It is possible, but using separate languages (as seL4 does) has certain benefits. For example:
- Kernel developers tend to have C experience. If the OS is writen in C, they have a much larger pool to hire from.
- Any such language would have to be acceptable both for the people who develop the OS and for the people who do the verification: I suspect it's not easy to find something that pleases both crowds.
- C compilers get better all the time. Every time someone improves the gcc code generator, seL4 automatically gets a bit faster. Less mainstream programming languages get better only if you maintain an expensive in-house team working on the compiler.