Were the electoral model to be abandoned, it would ensure that candidates would stick to major urban areas as much as possible because they would have the largest amount of influence per unit of effort. Now, this wouldn't hold true in all cases, but from what I understand the Electoral College as it stands helps to ensure that the sundry opinions of different interests in this country are given more consideration.
Interesingly, before the electoral reforms of the 1800s in Britain, seat allocations weren't decided by population, but rather influenced by the weighting of the needs of various regional trades/industries. While this seems very anti-democratic to modern American ideals, at that time industries were much closer to the individual. Also, I'm not so sure it was a bad idea: you baked lobbying and the concerns of industries into the political system as opposed to grafting it on in a shadowy, behind-the-scenes system, and therefore had the ability to regulate it to some degree.
The second reason is that it is not clear that a "secure, nation-wide popular vote counting system based on modern communications technology" is a good idea even before we get to the technology. Our system of government is a type of federalism (state/national) and moving to a popular vote based electoral system weakens this division. I don't have much expertise here, but can assert with confidence that expert opinion is divided on whether or not this is desirable.