This isn't a problem in practice though, you just get "strange" constants with units equal to some negative power of U in your equations. The same thing happens

This isn't a problem in practice though, you just get "strange" constants with units equal to some negative power of U in your equations. The same thing happens when you move from electrostatic units to SI: suddenly Coulomb's constant appears. Many people advocate ESU for precisely that reason: no Coulomb's constant.