The other aspect of having a low-slung action is that you won't hit the seam consistently. Big swerve in the air won't be anywhere near as effective without the extra lift that hitting the seam gives you.
On hip driving and whatnot, bowling quick is a game of transferring the momentum of the run-up into speed down the deck. Anything which gets in the way of that transfer is generally a bad thing, very few bowlers can shuffle and go whang (all shoulders, back and chest) as Thommo did. The hips are a flexible joint which, if you bend and flex them at an inopportune moment in the delivery stride, will get in the way of that transfer of power. The result is, apart from a loss of speed, your body contorts to maintain balance whilst trying to let go of the ball and the results are, generally, limbs and the flexible parts of those going in less powerful, more awkward positions. You grip the ball too hard or your thumb shifts at the very last second and what was a perfectly upright seam when your arm was at 9 o'clock in delivery naturally adds a little wrist twist or thumb movement at the very last moment. Again, you lose speed, accuracy and movement.
This is why I always found it a bit pointless when coaches would say stuff like 'get your front arm up!' at training if I was bowling pus. The problems generally start way further back in the process. On the front arm thing, also a bit of a furphy. It's a good idea when you're a kid/teen and still learning the bowling action and growing into your body but later on, it's about maintaining a strong body posture in delivery. You see it in every international bowler; early on they're reaching for the sky but as they get older, the front arm gets lower yet they're picking up speed. They realise it's more about that strong core, the front arm becomes more about balance than power.
Boxing and Kung Fu are two martial arts which really know how to punch and they realise the power comes from a 'closed' position at the chest/shoulders and 'heavy elbow'. Your need for a wind-up is less because you're using more of the big, powerful muscles (chest) and less of the small, weak ones (shoulders). It's also a more relaxed position; shoulders extended and high = more tension = less power = more pain at the punch's impact. Plus, the chest is heavily muscular so you're manipulating a more uniform mass of stuff whereas the shoulders are a more complex array of tissues which have more moving parts to coordinate, muscles and tendons move in different ways at different rates, etc.
Eventually you learn in both styles to keep shoulders low and relaxed and the consequence is (far) less effort required to punch, exponentially greater power and less impact pain. Same logic applies to bowling a cricket ball; keep your chest in and tight, stop your limbs from flying everywhere and it'll hurt less to let go of the ball and just, in general, bowl. It'll take less effort and you'll bowl yards quicker and, as your body is in a stronger position, the run-on benefits are better release positions so you'll get more seam, accuracy, etc. Honestly, it's a shocking revelation when it happens.