As king, whilst pretending to be Odin, Loki did the following:
Pardoned Thor, Sif, and the Warriors Three of their treason
Treated Thor as Loki himself had never been treated by their Father
Separated the two Infinity Stones in Asgardian protection, and gave one to another powerful being, for the sake of preventing both from being found at once or from making Asgard a higher priority target
Removed Asgardian troops from the rest of the Nine and kept them on Asgard, where the Space Stone was being kept and therefore where they were most needed, whilst also creating a time of peace for Asgard
Pushed Asgard toward entertainments (theatre) that aren’t violent
Rebranded himself as a hero rather than just allowing his identity as the Jotun Prince become all that would be remembered
And that’s just what was shown.
Turns out Loki, when in charge, puts up a huge statue of himself and then does sensible things.