“Jupiter’s gravity assist kicked it up (by 9K) to 45,000+ mph.”
The interesting misconception about gravity boosts is people think it increases the velocity of the space ship. It does not increase the absolute speed, all acceleration occurs to change the direction of travel. The force of gravity definitely increases the absolute velocity as the space ship approaches the planet, but as the ship travels away from the planet gravity equally decelerates the ship. At the end the ship is traveling at the same velocity relative to some “fixed point” but since the direction has changed, relative to its target, as far as the target is concerned, suddenly their relative velocities have changed greatly.
While what you are saying does make a certain amount of sense, there is one thing that occurred to me. Why would NASA use these objects if not the increase speed? You actually gave the answer, but didn’t elaborate on it. I think it’s interesting, so I will.
When we send a vehicle out into deep space, we are trying to send it to a target object. That target object may be traveling horizontal to us. It may actually be coming in our direction. Using the sling-shot effect, can help us achieve the best angle for the approach. It’s an angle that we couldn’t obtain on a straight shot path from Earth to the object without expending far more energy than we have on board.
This is a way to achieve that without increasing the delivery systems (and I’m not even sure that could achieve what we need to), and allows us to cut cost as well.