A few reasons that I could think of:
Having a cost associated with taking actions places a necessary limit on the size of the blockchain.
It allows for the exchange of value in unique ways. For example, requiring m of n parties to consent for funds to be exchanged. Or even using time-based encryption to release funds after time t.
Say you want to leave money for your granddaughter Suzie, but you don't want your evil son-in-law Stewie to keep it for himself.
Normally you'd have to have a bank or government to hold your money for some period of time, while they line their pockets with interest made on your savings. By writing a contract that requires some percent of the family to withdraw funds after 30 years, you can rest easy knowing little Suzie will get the money you left for her.
That's a contrived example, but you get the idea. Think of a multisignature wallet on steroids. That's an Ethereum smart contract that, by definition requires a store of value.
Ether can act as a reserve currency for ICOs. Random companies with nothing but a whitepaper and pretty websites are launching ICOs with Ethereum tokens, and the majority are worthless.
The list goes on. Decentralized applications just play really nicely with a decentralized currency.