Musk wouldn’t take it, or wouldn’t stay long if he did. People in cabinet positions get sidetracked all the time by stuff outside their main goals. For example, Dr. Steven Chu, secretary for energy under Obama’s first term, wanted to push a nuclear power renaissance. When BP had an oil rig disaster, he had to focus on that instead. So that’s great, we wasted the time of a doctor of physics on an oil spill. It’s far from the only reason the nuclear renaissance failed, but it didn’t help.
If Musk doesn’t realize this problem already, it won’t take very long until he does and leaves the job.