All equations speak of a relationship. The relationship is the same no matter what number system is used.
Deducing the hypotenuse of a triangle by using the equation a2=b2+c2 from the Pythagorean Theorem is the same whether you use metric or imperial measurements, why because we are speaking of a relationship. So if we changed the number system and the Pythagorean Theorem didn't work we would know that it doesn't really speak of a relationship and is invalid as an equation. Applying this to e=mc2 , I will pretend that I come from a civilization where we measure all speeds in fractions of the speed of light. Therefore the speed of light =1. Hence in my civilization e=mc2 becomes e=m . Since the equation was able to be reduced to e=m for a theoretical civilization who measure speed as fractions of the speed of light then it should be e=m for all civilizations because the relationship cannot change based on a number system. If there is another formula which is the correct one then perhaps that's the one we should be using.