>>12665297A Fire/Dragon type would have been weak only to Ground and Rock attacks.
Since Charizard is the final evolution of a starter, and moreover, the final evolution of a starter in the first games of the series, having an elemental triangle that works like a rock-paper-scissors game that break itself would have been really stupid.
Gen IV pretty much did this, but it was the forth game in the series. If you want to break a basic concept, you first have to build that basic concept.
The same goes with Gyarados: if it would have been Water/Dragon it wouldn't have any weakness in gen I.
Also, Dragonite's family was supposed to be some super-rare shit, so if any fisherman or little kid could have a Dragon type they wouldn't be so special.