Problems with replacing Ionic spark with Shiv or Tiamat:
Very few of the champs that actually needed an Ionic spark synergize with Shiv or Tiamat, they were generally off-tanks who wanted to push lane and benefited from AS, such as Shen, Volibear and Irelia. However Shiv scales with crits and AS, crits effectiveness increase exponentially with other crits (ie they aren't worth jack until you have multiple crit items as Xyltin stated above when talking about avarice). They also scale more with attack damage. Both of these stats are things that people who actually need to or should buy an aoe item to split push with don't want. Tiamat is the same it scales with AS and flat damage meaning that its weak on the champs that used to buy Ionic spark. ADCs (which this item fits into mostly) don't need split push capacity they should be in team fights and even if they're not, by the time they have all the items to scale up the shivs damage they 1-shot creeps anyway meaning that it barely makes clearing any faster.
TL;DR: Stats and scaling on both Tiamat and Shiv are useless on the majority of champs that its actually a good idea to get the effect on ie split pushers like Shen.
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