A Republican in CA, IL, or NY would have far more incentive to vote. Same for a Democrat in WY, UT, or OK.
In a real sense, with a popular vote, the entire nation would collectively decide who governs the nation. That approach makes sense to me. And you would get more of a say in that case, not less.
As it is now, the matter is decided state by state. In that system, whether your vote matters at all depends on where you live. And that's true in at least two ways. First, I think it's relatively safe to say a Republican's vote doesn't much matter in CA, IL, or NY. Same for a Democrat's vote in WY, UT, or OK. The result will be the same whether that voter votes or stays home. Second, the electoral college creates a relative weight problem that gives more power to certain states. For example, CA gets one vote in the electoral college for every 718,909 people. MT gets one for every 360,000. It's as though every vote in MT really counts for two CA votes.
I'm not convinced there is anything obviously superior about the electoral college. And I am not convinced, at all, that a popular vote would somehow mean CA and NY would govern the entire nation.