The lore explanation would be that the flight assist is constantly firing thrusters to correct the ship's velocity such that it is going at the speed you set with the throttle and in the direction you point it.Though what I still don't understand is why boosting increases your max speed
If you set flight assist off and put the throttle at 25% you will slowly accelerate because the engines are constantly firing forward, albeit at low power. Now when you set flight assist on and maintain the throttle at 25% the flight computer will decrease the engine power and fire reverse thrusters to keep your forward speed constant.
When you boost you tell the flight assist that you want maximum speed and thus it doesn't need to regulate engine power or fire reverse thrusters. You end up accelerating forward at full power for as long as the boost lasts. Then when the boost period ends the flight assist begins firing reverse thrusters again to bring your forward speed down to match your throttle setting.
None of which explains why, if you boost then switch flight assist off you don't continue accelerating. That's entirely down to a game mechanics decision, as described by other posters.
Game mechanics and lore are orthogonal concepts and often contradict. Personally I don't care that the speed is arbitrarily limited. It's true that everyone complained in the game's test phase and I have no objection to it being changed. What I object to is being told "the system works like this" and then seeing that it doesn't.