Some not-very-well organized thoughts that take up too many screens...
There have been more constitutional amendments introduced in Congress to abolish/reform EC (including as recently as 1997) than any other matter. Criticisms of EC are numerous, widely held and few folks (that I'm aware of anyway) think that such a method would be chosen today.
Representatives of less populous states have consistently opposed proposals for direct prez election. EC doesn't come close to weighting states according to population. CA population is more than 60 times larger than WY. However, California's 54 EC votes make it only 18 times more important than Wyoming's 3 EC votes.
Large state reps have also opposed change because winner-take-all electoral votes in 48 of 50 states (Maine & Nebraska are exceptions) place premium on heavily populated competitive states that get disproportionate share of attention. Swing voters in FL, Michigan, Penn, for example, become very important and candidates are driven to spend lots of time, resources, media efforts in such states.
House actually passed (by necessary 2/3rds) direct election amendment in 1969/70 after Wallace candidacy threatened to deprive either Nixon or Humphrey of EC majority (Wallace got 46 EC votes). Birch Bayh (probably strongest congressional advocate of direct election in last few decades) marshalled growing Senate support. Southern senators - blathering on about "federalism" and "state rights" - led filibuster that killed proposal. Similar arguments by senators from many of same states would probably be made today (not to mention state legislative role, however much that tends to be formality). [[fwiw: May not be surprise that Bayh was from state where prez winner can generally be predicted. Rep almost always wins Indiana. Neither Dems nor Reps make many campaign stops in Hoosier state: not worth it for former and not needed by latter.]]
While direct election proponents point to EC as obstacle for minor party candidates, major party opponents of DE warn that growth of "splinter" parties will lead to fragmentation of US politics (can't you just hear those crocodile tears?) blah, blah, blah. Interestingly, given situation this year, latter also express concern that DE could lead to increased temptation for fraud in vote counting, resulting in prolonged recounts and chaos.
Other than dependence upon mass frustration as vehicle for change, growing potential electorate for "other" candidates as indicated by public opinion data seems only be basis upon which to develop strategy to get rid of EC assuming goal is worth time, effort, and resources. On other hand, percentage of "pure independents" (those who place themselves completely outside Dem-Rep framework) has increased only a few percentage points in last several decades.
Re. EC reform in which electors would be apportioned by popular vote - ostensibly eliminating "faithless electors," lessening influence of strategically located swing voters, weakening one-party states, increasing likelihood that winning candidate receives most direct votes - opponents have claimed that such change will weaken influence of people living in large cities who (so the argument goes) often hold balance of power in prez elections. Same thing goes for proposal to have all electors chosen by congressional districts.
On slightly different matter, not only is EC indication of anti-democratic framers, it is good example of less-than-wise framers As conceived, electors (most of whom were originally chosen by state legislatures) were expected to act somewhat independently in voting for 2 persons they thought "most qualified" to be prez. Framers expected most electors to cast one vote for someone from their home states. thus, votes could be so varied that absence of majority for any one candidate would be commonplace. And that would mean House option regularly coming into play.
Framers' method of selection did not account for political parties running prez-vice prez ticket with electors pledged in advance to respective slates. System broke down in 1800 when Democratic-Republican prez candidate Jefferson & DR vice-prez candidate Burr received equal number of EC votes. 12th Amendment followed. Michael Hoover