Fire beats Ice as well.. There goes your theory.
Also, Electric is not unbalanced. It's got one weakness, but how many resists does it have? Just three: Steel, Flying and Electric itself. Using a Flying-type against an Electric-type is dumb and most Electric-types have abilities like Volt Absorb, Motor Drive, etc. Meaning that aside from Steel-types, most neutral match-ups don't worry about resisted hits.
Damn forgot about Ice.
However, it only supports my point that Fire doesn't need another advantage anyways, since it already has the most out of the starter types.