Is Goku still pure-hearted?
Well as far as at the end of DBZ, we can concluded that all of the saiyans including Vegeta are pure hearted. This is because one of the condition of the Super Saiyan God transformation was that 5 pure hearted Saiyans needed to come together and since the transformation worked, it can be concluded all of them are pure hearted post Z.

Secondly, The Omni king isn't powerful in terms of raw power. What makes him terrifying is his position and the ability to erase anything from existence. Even the angels and  the grand priest and of course the gods, the strongest beings of the universe bow down before him so what makes you think Vegito blue could stand up to him. 

Goku on the other hand has no evil in him. The only reason for him wanting the tournament is his addiction to battle and at the same time his rather naive and careless nature could be considered at fault for the tournament of power.

However, it was implied that goku did actually do the other universes a favour(Although he didn't intend to) as Zeno was about to erase the rest of the universes with a lower mortal  ranking.