You can't just slap some zeros onto the start of a v4 address and come up with a bigger address space that somehow works with v4 networking code. The problem isn't backwards compatibility, it's forwards compatibility: v4 isn't forwards compatible with larger address spaces, so it's not possible to do what you're suggesting.

There are various ways of making a bigger address space with backwards compatibility to v4 though -- and all of the ways which are actually possible and work are already implemented by v6.

The majority of packets on the internet pass through fairly hard-coded switching chips that probably couldn't be updated to handle this. They can handle IPv6, though.

If it were made truly backwards compatible

It can't be made backward compatible. Every switch on the internet needs to understand your new extended address scheme otherwise they'll send your packets to a dead-zone somewhere in Uzbekistan. Backward compatibility was never an option. As soon as you add new bits to the address, old routers won't send them to the right place.