Staying on the ship and not showing himself despite the cloak, will make him look even more sus than even this much. It's like a bare-minimum greeting to the soldiers, so they don't automatically assume he's hostile from the get-go, after providing vessels that annihilated an entire invasion fleet.
If MC's priority is to keep his identity secret, there are risks for going outside. Some likely and some unlikely. Wearing a robe won't guarantee against people seeing MC's height and build. There could be a glimpse of hair, skin color, or gender through the sleeves or hood. Someone might hear his voice, or hear his slaves or friends say his name when he's talking to them. Maybe a gust of wind, or a city spy casting a spell, could lift the hood and reveal MC's face.
What are the benefits for MC to go outside in a disguise? Maybe the city government and people will be less apprehensive about the unknown mage. This may benefit the city, but it won't benefit the MC. As far as anyone knows, MC and the unknown mage are different individuals. The reputation of the mage doesn't affect the reputation of MC. Unless MC wants to use the mage as a recurring alter ego, but MC keeps saying he's not going to participate in anymore events like this. Of course, I assume the author won't allow MC to do that.
Maybe if the city government was less apprehensive of the mage, they'd be less likely to torture or blackmail the female adventurers into revealing the mage's identity. But if the government was already capable of doing something like that, I don't think seeing the mage walking around the city while hiding his face would change their mind. Now that I think about it, it would be better for hiding MC's participation if the adventuring party didn't reveal themselves either. After destroying the blockade, they could have landed somewhere else and walked to the city sometime later. Then no one would know that the adventurers were responsible, unless one of the girls talked.