In most games, the runner will only play a portion of the cards they draw, if for no other reason than that there are only 4 clicks in a turn and you don't get to stack your deck. Thus, given that some number of our draws will be naturally dead for other reasons (lack of time/money, duplicate consoles, etc), most successful runner decks have, at least implicitly, developed strategies to deal with useless cards, generally by efficiently drawing even more cards. In essence, most successful runner decks are already "pre-teched" against your strategy.
Considering the games I've personally played where the corp only draws 1 or 2 types of ice, it seems like the most common outcome will be that the runner spends the majority of the game with an unused tutor or icebreaker in hand, happy to trade their lower hand size for the savings in time and money.
edited repeatedly for grammar