You could in theory create a centralised electronic currency with all the hashes computed. But then how would you distribute it? Chicken and the egg. How do you get people to use your currency if you have all of it? Do you just give it out to people? But what system. If you're giving it away it has no value. It cost you nothing to create it. etc.

Mining also solves the distribution and creation of value problem. People won't use your currency unless it has value. To have value it needs to have a market to use it. To have a market you need people using it. Mining creates an incentive to create it since it has some value. And mining means the currency is distributed to people who create value for the system.