Distributing electors by state wasn’t the “intended effect” of the EC. Nobody proposed direct election of the President. The choices were between having Congress elect the President, and having a separate Electoral College. It arises out of the fact that the framers viewed us as a collection of separate states and so it made sense to do everything at the granularity of the state. The executive branch of the European Union is indirectly selected for the same reason.
As to the intended effect of the 3/5 compromise—what would have produced the result that some people want is for slaveholding Virginia to have won that debate, because it was the one that wanted proportional representation in both houses.
They're all ways of making a decision. In the end the votes are tallied somehow, to some goal. We used to have different goals 100 years ago.
No, what is broken is indirect election with voting power distributed by state (no matter how you allocate the electoral votes based on the popular vote in the state, whether its winner-take-all, by-congressional-district with winner-take-the-extra-two, or proportional allocation), since the basic model, irrespective of allocation, creates a intense systemic incentive for voter disenfranchisement within states, since by disenfranchising people in your state that aren't likely to vote like you, you not only nullify their vote (but reduce your states overall vote) as you would with direct election, but seize their voting power for yourself (well, at least, redistribute it among those you do not disenfranchise within your state.)
This is, of course, the intended effect of the EC and 3/5 compromise, with the original focal disenfranchisement being chattel slavery. But it works even more powerfully without chattel slavery, because then you don't have the voting power from the disenfranchised population deweighted the way the 3/5 compromise did.