I would guess that it's mainly scale. Our largest constituency by people is about 110,000 and by area about 4,500 sq. miles. When you're dealing with "constituencies" of 40m people or 500,000 sq. miles then you are coming into logistical difficulties to do things quickly.
If voting and counting were all done over a period of two weeks and they were counted as you went then they probably could. But that probably throws up its own problems in terms of secrecy and leaks. And I guess you make the decision that doing things properly (I know, I know...) is more important than doing things quickly.
For historical context, that's exactly what they used to do. Voting went on for months, and the gap between the November election and the inauguration the following year only exists because historically the admin took so long.