Why is the Ampere the only SI fundamental unit for electricity?
Volt is defined as Work done for unit charge. Charge can be derived from product of current and time. So volt can be expressed in terms of mass, distance, time and current. 

Now for ohms, it can be defined as the ratio of voltage and current. So it can also be expressed in terms of mass, distance, time and current. 

So with just a unit for current combined with other fundamental quantities, we can define all the other electrical quantities.