What's the point of Jesus's miracles?

It's pretty popular to think of Jesus's miracles as simple demonstrations of who He is i.e. His power over sickness, demons, creation. This means that Jesus's main goal with miracles is simply to demonstrate that He is who He says He is. I wonder, though, whether this is a too-reduced view of the miracles.

It seems to me that the miracles do not just simply show us the power of Jesus (though they do do that!), but that they demonstrate the nature of that power and what it is for. In other words, the miracles of Jesus do not just show that Jesus is Saviour, but what kind of Saviour He is and what kind of salvation He is bringing. If Jesus was interested in simply showing sheer power then He could have done things that were more obviously spectacular (Muhammed apparently split the moon in half!). Instead, He does things that have meaning for the kind of salvation He brings.

His miracles have a purpose; that is, they reveal the kind of world He's making. The miracles are essentially the future kingdom or new creation at work now. They are signposts to a renewed world. They are the renewed creation breaking through - a place without sickness, without evil, without death and a place where we will flourish under the King. The miracles show the Creator standing in the middle of the fallen world and starting to renew it and re-order it according to His intention. So, the calming of the storm does not just show that Jesus is sovereign over creation, but depicts the Creator re-ordering the hostile elements in the cosmos for the sake of His people (represented the disciples!). Jesus is renewing the world for His people. It's looking forward to the re-genesis of the world.