The original poster said they were worried about this leading to "highering illiterate officers"
Mis-spelling the word 'hiring' as 'highering' when expressing a fear about falling literacy standards in the police is ironic, and therefore funny.
Further elaboration was not warranted, but I'm providing it as a public service.
No, nobody ever says “I’m going to higher you” as a way to indicate they are promoting you. Not in the military, not in non-profits, not in the government, and not in any private or public business in the US.
“Higher” is a homophone with “hire” and “hire” already has a critical role in reference to career management.
At this point I can only assume you haven’t worked somewhere where English is the spoken language.
Highering is an existing, valid word, and it fits the phrase.
https://en.wiktionary.org/wiki/highering
I agree that it is an unusual choice, but that doesn't mean you can assume it was a mispelling.
Moreover, the meaning went through. Ultimately, the word itself does not matter, and none of your explanations are relevant.