Why is blockchain necessary?
I think the introduction of block has much more a security-related origin:

Currently, getting transactions confirmed costs a certain amount of work for which computer have to run a long time and cost some time, effort and money. Because of this, it is hard to manipulate the chain of transactions. It is hard to find a correct block with a certain set of transactions and cheating will result in your block being refused by the network.

However, when clients just keep lots of transactions, it would be much easier to f.e. set up thousands of false nodes that manipulate the network. A node that only requires memory is much cheaper than one that requires hashpower. With some resources it's easy to add thousands to hundreds of thousands of clients (these don't have to be separate machines but can be virtual ones) participating and entering bogus transactions or leaving some out.

The fact that creating the blocks is "difficult" add a lot of security to the network, making it extremely hard to falsely manipulate the transaction history.