If there were no way for an elector to vote for someone other than the state's choice, there would be no purpose in having formal electors and votes. Instead, the government could just total the votes from election night and call it good. The founders put this safety net into place to protect people from making an incorrect decision.
No, Electors should not be able to vote for someone other than their established State nominee. That is the very basis of the Electoral College system. If Electors are allowed to vote for whomever they choose, we should do away with the Electoral College altogether and judge elections by the popular vote alone.
If Electoral College members are allowed to change their votes, it undermines the entire election process. The Electoral College should probably be reformed or abolished, but for now that is our system and it should be respected. Electoral College members changing votes would cause worse division and conflict than already exists in America.
In the electoral college system, electors should have to vote for who their state voted for. However, that is beside the point. The electoral college system is anti-democratic. Each person should have one vote. We should not have "electors" and "swing states." None of that should matter. Each person should have a say.