True, but then we have to account for Prime Kim dying and being replaced by Phase-shift Kim. Per Starfleet protocol, that crewman has to start from the ground up. That process runs roughly 4 years just to make it from cadet to ensign.
Are "Phase-shifted crewman" even considered in Starfleet protocol? It's not a "Mirror, Mirror" parallel universe, it's just a light time variance. They should still be considered starfleet graduates, if it's a light phase/time-shift and not a parallel universe... I think?
Honestly what is the point of a promotion when you are stuck on a ship 70 years from home and money no longer matters anyway?
He's not going to get paid more because there is no pay and hes not going to get a significantly different position on the ship because the talent pool is limited to the ship itself. so the "promotion" would just be performative anyway.
Once they return to earth there would be some tangible benefits
which is convenient because then he DID get a promotion to Lieutenant and took over as chief of security and tactical officer. Eventually he was promoted to Commander at star base 11