Unfortunately, tax codes cannot simply be streamlined to be more algorithmic because every company has different facts and circumstances, which ultimately require judgment calls.
If you tried to build an algorithm that accounted for all of the complexities, you'd just send the problem upstream (who writes the algorithm?).
You mention Apple's Ireland operations, and you allude to the "earnings stripping" that is commonly achieved through such foreign companies. In some cases, the subsidiary is a pure tax play. But in other cases, it's simply a matter of having foreign operations that perform services that are charged out to affiliates in various countries. Deciding how much to mark up these services is a classic facts-and-circumstances inquiry. There's no one-size-fits-all rule that can adequately capture the spectrum of activities.
Compounding the problem is the fact that there are multiple taxing authorities involved, and if one gets greedy then others are affected (through foreign tax credits, for example). Sometimes a company just ends up getting stuck in the middle of a turf war between tax agencies in two countries.
Lastly, Tim Cook does have a "moral responsibility" with regard to taxation: maximize shareholder value. Granted, he could reasonably decide to take actions that do not minimize tax liability in the near term, on the grounds that he would generate goodwill with consumers and increase sales. But if he announced that he was going to dismantle Apple's foreign subsidiary structure so that Apple could pay more taxes, you can bet he'd face shareholder lawsuits in no time flat.