There is two upsides to this: 1.) All quantities are order one, safely away from underflow and infinity. 2.) The equations are generally simpler, which was important when the many limitation in simulation codes was flops, not memory bandwidth.
There are also important downsides: 1.) You have to manipulate the equations before you start coding. Porting features from a code that used another normalization is quite error-prone. 2.) All quantities are order one, which makes it hard to detect if you accidentally use and electric field instead of a magnetic field. All you see is a number of roughly the correct magnitude. 3.) Comparison between codes is more difficult, in particular if the use different normalization, because you have to convert from "code units" to actual SI units.
https://books.google.de/books?id=uzJbyD6_3DAC&pg=PA4
And yes you have to be consistent and stay in that unit system. The other remaining two we used plain Kelvin for temperature and for the charge Coulomb was measures in electron charge. That's it.
If you have a process that converts floats into other formats with more restricted exponents, like human readable strings, it might matter.