Running a full node (downloading the blockchain) allows a user to interact with the network, without having to trust any other network participant.
For some users, this may not be important, but for many users it is very important. For example:
- You are a business, and you need to ensure that txs you send and receive are in fact being communicated across the entire network.
- You run an exchange, and want to make sure large deposits are not going to be double spent or orphaned
- You hold a large amount of cryptocurrency, and want to maintain security and privacy of your funds
- You live somewhere with heavy financial/economic restrictions, so access to webwallets, etc is banned outright. So to interact with the network you have to run your own node.
- You are a believer in the philosophies behind cryptocurrency, and want to run a node just to help the network grow and remain robust.
This is not an exhaustive list, I'm sure there are more reasons than I have listed. In general it is important that users remain capable of running their own nodes, as otherwise they will have to trust someone else to do so for them.