Drake's character and actions are not an incongruity.
How many motherfuckers does Master Chief blow away? Yet we don't have this conversation about him despite the fact that he is, tacitly, presented as an equally throughout-Good character. Arguably even more so than Drake is. 'But he's at war'... and Drake is acting in self defence, and had the pirates not been there, he'd have shimmied through the locale without harming anything. What's the difference?
Also, has the Pulp inspiration been lost on people? This particular depiction of morals is more to do with staying true to that genre than anything else. It's an action romp. Of course he's 'shooting the bad guy'. Criticising the game for that is about as good as criticising it for depicting him being greedy enough to go treasure hunting.
Wakey wakey.