Turnout would certainly be higher, but it's not clear that it would be a "better" representation of the country.
The electoral college distribute power, to some degree, based on geography. Geography is correlated with a large number of other "diversities" of American culture, from race, population density, to industry, to global warming risk, etc... Switching it to a straight majority would take power away from all of these subsets of society.
This election, it seems, it was "white rust belt" Americans that decided the election. In Gore vs Bush, it was Florida. Next time, it will be something else. It's all highly imperfect and somewhat random, but I see danger in solidifying power in what essentially will be people who live in cities.