4-S is pretty much right on with his comment, so I'm just going to vote up some random answer of his somewhere else because I can't vote up a comment.
Now then, you should also note what generation Rhydon was introduced: Gen I. And Rhydon was in fact one of the most powerful Pokemon of that generation, an amazing feat in that Psychic dominated time. Grass was pretty much non-existant as an attacking move back then, so that didn't cause it much trouble. It has enough defense to survive Eathquake. Fighting was also pretty non-existant, and Steel wasn't even made. Back in Gen I, Pokemon were also able to utilize Special moves due to the way EVs were done. Rhydon could be seen using Fire Blast and Blizzard a fair amount, so of course it will have their weaker yet more accurate counterparts. Surf also saw some use on it. As for the Water and Ice weakness, there needed to be some balance to Rhydon's awesome strength.
Try looking at the Pokemon from the generation that they were introduced. Rhydon was an incredibly powerful force in Gen I. It would not make sense for Game Freak to remove those moves or change Rhydon's typing (Note, Magnemite and Maneton just got a type added on, and kept the original type as well). They have tried to give Rhydon some things so that it wouldn't fall into oblivion, like the uncommon move Megahorn, an evolution, and Eviolite.