Yes he did. Shanks offered Blackbeard a fight. Blackbeard turned it down. Akainu was concerned enough about Blackbeard he personally wanted to kill him when trading for a ship.
And we are talking about the character that kills marines for not fighting. We are talking about a guy who blew up a ship full of civilians and children on the off chance 1 "bad guy" escaped.
akainu absolutely is the kind of person fascist governments would love to have lol.
There's a difference between a battle cry about killing the enemies you already at war with and starting a new war. I'm sure you're smart enough to understand it. If is "kill all pirates" was literal, he would have jumped on the shichibukai throat
He showed he actually cares about stuff like the Navy's overall manpower even though he kills deserters. If he jumped on Shanks throat, that would be a new war against a fresh emperor and his strongest crewmates. Even if the Navy ended up winning, they would take more losses which would weakened them even more.
So that was not his decision to take, but Sengoku.
Akainu is a cold-hearted and a fanatic. But he's not without reason.
The series highlighted several times how important manpower is, yet you INSIST that it doesn't matter. Sengoku didn't declare war against Shanks? Akainu didn't immediately jump on his throat? That means the Navy couldn't beat him and his crew.