In light of the recent update for boarding, I like think this idea could be expanded upon further. Currently, torching the core ejects the player, thereby disabling the ship. I like the idea that if implemented, this would let you either go for the core, disabling the ship (and turrets) and allowing you to gain control but leaving the player to come after you, or B - attacking the player directly, leaving turrets and ship systems working and forcing you to go back to the core to gain control. So, if implemented and used in a ship, you would need to both disable the core and capture the cockpit to take a ship.
The core should not be removed. But neither should it serve the same purpose it always has had. Sure, asteroids and stations don't have cores. But neither do they fly around. Having cores makes sense on a ship. They shouldn't necessarily be buildblock and entry point, but rather a key vulnerability. Make it so that disabling a core disables all connected systems (and all AI's on docked turrets). So a ship could have it's core taken out, either by boarders or clever shooting, leaving shields, armor, and power intact but forcing players to use computers for weapons. After all, it's the core of the ship.