Well the President can already pardon someone for killing his political rival, the only question at hand here is whether the President himself can order such a thing and face no legal consequence.

Not that it's going to happen. USA remains a democracy. Even with blanket immunity, a President, and indeed his party, rely on votes to remain in power, or at least remain in opposition. If the President were to commit a criminal act that is hard to argue is "acting in the office" and face no legal consequences, he and his party are highly likely to still suffer massive political consequences. So it's not like the President is King. Nobody votes for a King.

The President still has to act in a way that the American people can tolerate. Trump pushes that close to the limit, but even he wouldn't get away with murder.