Cosmos IBC and the argument for application-specific chains

It makes some intuitive sense that blockchain interoperability should be a useful technology — after all, today, there are many different blockchains (with varying levels of use) that don’t communicate with each other. It’s easy to imagine a future for blockchains where multiple different networks are isolated from each other in some sense but would ultimately like to talk to each other.

The description above is vague on purpose. What are the exact reasons for anyone to build their own blockchains and what does interoperability mean?  Blockchain interoperability has been an area filled with poorly defined ideas about what kinds of blockchains should talk to each other and why. As such, many of the first generation projects that purported to “solve” this issue have failed.