If we agree that the states are different (somewhat different laws etc), then, to me, it seems logical to me that the people living in different stats have different views, opinions etc that they are more likely to have in common with other people living in the same state than people living in other states.
To me, it also seems logical that the people who chose to not vote are more likely to share the views of the people who voted in the same state (to me, not voting means "I don't care" and I would assume the default views for your area). Children cannot vote and I would assume that their parents know what's best for them.
In my opinion, the different views of the states should be represented (otherwise just scrap the "state" division and have one big government for everyone). This is done with EC in that all states get at least 3 votes irrespective of their population. So, smaller states get more votes than they would if the votes were based just on population so that they are not overshadowed by bigger states.
Popular vote really depends on turnout and I assume that convincing more people to come and vote for you is easier in a state where a lot of people likes you (for example, California for Clinton) than it is to convince the people of some other state to vote for you.
This means, that with strict popular vote, all, say, Clinton, has to do is to convince a lot of people in California to come and vote (to win California vote by a bigger percentage) to offset the votes of entire smaller states. As it is right now, whether 51% or 80% of Californians voted for Clinton, she still gets the same amount of EC votes.
Also, with popular vote, the opinion of those who chose to not vote is assumed to be with the majority of the entire country, not just their state, which is not completely correct, given that people in different states have different majority opinions/problems.
In short, popular vote would require convincing people in areas that like you to go and vote more, while with EC you need to convince people in more areas to vote for you.
Take the EU for example - the EU does not have an elected President and the elected positions are divided by country (each member country gets some number of seats). However, if there was an elected President, then the elections would have to be done with something similar to EC, otherwise the opinion of Berlin (one city) would matter more than the opinion of one or two Baltic countries (where people and conditions are really different).