So rather than tyranny of the majority, now we have tyranny of an arbitrary minority. I fail to see how that improves things.
As others have pointed out, the constitution and the court system are the features that are supposed to counteract tyranny of the majority, not the EC or the Senate. The EC and the Senate aren't there because they make the system better or more democratic, they're there because they were part of the necessary compromises that were made hundreds of years ago to convince all the independent states to band together into the United States.