Here (NJ) we have a 'Rehab' section within the statewide Unifior Construction Code. That allows certain things that do not affect any life safety, to be replaced without conforming to 'current code requirements'.
Keep in mind that this is a New Jersey Code(Law), and may not apply in your area.
That said, replacement of plug fuses that can be 'overfused' with circuit breakers, properly sized is an improvement in safety IMHO.
Also, something that was inspected for code compliance when it was installed (original) is still OK, as long as it is not altered or presenting a dangerous condition.
Again, out of curiousity, where did you arrive with the "60 amp minimum"? From load calculations, or is that a local requirement for apartments?