The 13 largest states can already determine the outcome of a presidential election on their own without monkeying around with the process, so I don't see what they have to gain by it from a collective standpoint.
Yes, 13 largest states could already determine the outcome of elections...but not all of them lean Democrat...although most do. What they gain is the elimination of the advantage small states have in the Electoral College. Let me explain.
Each state gets 1 electoral vote for each Senator and each Representative they have in Congress. Every state, regardless of size has two Senators. The number of Representatives is determined by population, but each state, no matter how small has at least one. A number of states, Wyoming, for example, are small enough they have only one representative. My home state, Colorado, is large enough that it has seven Representatives, although it is still a small state.
Now look how that works in the Electoral College. Wyoming, which has 1/7th the population of Colorado, has 3 Electoral votes (2 for its Senators, and 1 for its Representative). Colorado has 9 Electoral Votes (2 for its Senators and 7 for its Representatives). So it ends up that Wyoming, with 1/7th the population of Colorado, ends up with 1/3rd the amount of Electoral votes. You can make the case that 'this is not fair'...but the Electoral College was designed to protect the small states, and it works exactly as designed.
What the Electoral College does, is make the small states, which tend to vote Republican, more important in a Presidential Election. That is why large, liberal states like California want to get rid of it.