Yeah, no. Even putting aside my usual arguments of "flaws give things character" Ice is one of the absolute best offensive types in the game. Pretty much anything that can learn a decently strong Ice move will run that recently strong Ice move semi-regularly. Even defensive non-Ice Pokemon will often run Ice Beam instead of an actual STAB. Giving Ice-type Pokemon an actual defensive presence has the potential to break Pokemon like Avalugg that were designed with minimal resistances in mind (keep in mind Avalugg, despite its poor defensive typing, has still seen genuine high-tier play, just because it's that bulky).Give two more resistances for Ice, and those resistances must be important. No more, but no less.
Consider Ground, another one of the best offensive types in the game. It also has a very respectable defensive profile, and its blend of offensive and defensive excellence make it what I would argue is the best overall type in the game. Game Freak seems to agree with me, as to balance it out, Ground has more ways to negate its damage than any other type. It has a natural type immunity in Flying, a common ability immunity in Levitate, a unique held item immunity in Air Balloon, and a unique move immunity in Magnet Rise. On top of all that, its best move can also be neutered by Grassy Terrain.
Unlike Ground, Ice is incredibly spammable, not only because it has no ways to completely negate its damage, but also because most of its moves come with a random 10% chance to OHKO the target.
Altering the type chart is not nearly as simple as many people think it is.