What are the benefits of ‘sharing’ a computer?

Why is a singleton computer valuable? Wouldn't i want to have my own computer that I can choose to make connections through when desired? Isn't the 'inter-net' between independent computers an approach that is already flexible and useful as is? What tool is ethereum replacing or making more valuable? I struggle to understand the value of one 'singleton' processing system….. I have to use the internet to reach the ethereum network so how am I achieving something new or useful? Is it an expensive network of websites/ applications that could easily be built with other protocols? Is ethereum just a cybersecurity protocol? Is ethereum a philosophy that supports a dev language(solidity)/culture of building applications that run by themselves?