First of all, Akainu's obsession for Luffy comes from Luffy being
Revolutionary Dragon's son, not because Luffy being a famous pirate. So, you can say Akainu only wanted to kill Luffy because Luffy was the son of the Revolutionaries leader, not because of being a pirate.
Another
Revolutionary Dragon mention;
Why he is obsessed with Revolutionary Dragon? Surely, it should've been a political view that Revolutionary Dragon wants to overthrow the Government, which Celestial Dragons controls over it,
why Akainu cares about this, when other Admirals doesn't care as much as him?
Dragon is not a pirate.
Because Akainu is the one of the top dogs of the government, protector of Celestial Dragons, he only cares about destroying the enemies of the government, not pirates. If he had problem with pirates, he would side with Fujitora about the Shichibukai removal decision, Akainu could at least stay neutral and say nothing about that, but see that Akainu
wasn't even neutral about Shichibukai removal decision, he sided with that
Shichibukai Pirates that they should've existed still.