Consider the analogy of your house address. One day you decide to change your address from "123 First Street" to "1600 Pennsylvania Avenue". What difference does it make outside your own property lines? None - because the rest of the world still behaves as if the physical location of your house didn't change, the name of your street didn't change, the city name didn't change, the zip code didn't change... you get the idea.
Mail, packages, and so on will be "routed" to your house based on its location in the address network of your community. The number of your house (computer), by itself, is only the last and final stop (network hop). Everything along the way has to agree, has to synchronize, and you only control the very end of the path.
You can number your house (or computer) anything you want, but for your network traffic to continue to flow you must do so in sync with your environment. To change your house address, you would have to change its number, AND get the bureaucracy to change the name of your street, AND change the name of your city, AND your zip code. Likewise, to change your IP address to something outside your allocated block, you would have to change its number, AND get your upstream provider to change your allocated block, AND change their routers to route that block to you, AND advertise that via BGP to their routing peers.
In both cases you are synchronizing your change with the outside world so the outside world knows how to find you. Otherwise, the effect is that network traffic can't find you anymore - and the only entity affected by your change of address is you. Which, architecturally speaking, is a good thing!