Actually, at the time of the launch the object is probably going away from us. So a straight line trajectory from earth includes the angular velocity of earth at the time of launch which unless the ship was launched at the perfect mathematical time, will not direct it in a vector that will intercept the target without burning a lot of fuel. But if you can use earths angular momentum and direct your craft to another object that will just happen to intercept your ship, then using small thrust manuevers you can redirect your ship to take advantage of a gravity well, to redirect your vector years after takeoff in a direction towards your goal with almost no fuel. The fuel use is trying to overcome earths angular velocity, which you get for free banking around a planet.
Yes I agree. I’m not a scientist or mathematician, but this is all very logical. That’s where I approach it from.