I think you make two big mistakes here.
First, you assert that without the EC, candidates would ignore small states. This mistake is rooted in two problems: One, they already ignore small states. The EC doesn't favor small states at all. It favors swing states. Two, without the EC, there would be no reason to ignore small states, because state lines would no longer be relevant at all. A vote in Wyoming would be just as valuable as a vote in Illinois.
Second, you assert that if candidates don't address local issues, voters will have no incentive to vote. That also doesn't make any sense. Do people still vote in Alaska? Hawaii? Montana? When's the last time any candidate spent significant time addressing issues in those states?
Any disincentive to vote is rooted entirely in the fear that one's vote will be meaningless. Republicans voting in California, Democrats in Wyoming, etc. These folks might very well feel it's a waste of time casting a ballot for President, since they already know how there state - and therefore the EC votes tied to their own personal votes - will be awarded. And this disincentive therefore only exists because of the EC, not in spite of it.
If we switched to a national popular vote, then every Republican in California and Democrat in Wyoming could vote for President knowing that their vote actually would have an effect on the outcome.