Back in the day, the US was more of a federation of states rather than a single nation. Quite like the EU is now. Each state was a quasi-nation of its own, and the federal government was intended to just sort of administrate that federation. So, the president was voted on by the states, not by the people, because he had basically nothing to do with the wants and needs of the people. He was just a designated treaty signer and funeral-goer. Just as with the congress and senate, the quantity of electors was designed as a compromise between the large powerful states and the smaller states. It was kind of a brilliant compromise, for the time.
Now, however, as a cohesive nation with nationwide media and national parties, the EC does nothing but cloud the election. Frankly, we are kind of past the idea of even having borders. We would much rather our opinions are represented in government rather than our geographic area.
Why is the run-off in a different format? Presumably, they didn't think it would happen very often, and if it did, allocating votes to Congress the same way they did to the EC would result in the same result. One vote per state would hopefully assure a clear winner.