...you can download only the files that you need, and no need to download everything with it.
To do this, you would need to trust that you are receiving the correct files (blocks) from your peers. If they lie to you and serve a false history, how will you know?
A full node downloads the blockchain so that it can independently validate the current state of the network, starting from the genesis block. By working through the network's history, the full node can verify for itself what the current state of the network is, without needing to trust any peers to not lie.
A lightwallet can download just the block headers (80 bytes per block) and use them to help verify that the wallet's transactions are authentic Bitcoin transactions.
But in both cases the node/wallet must have a full history of blocks/headers in order to not be trivially taken advantage of. So I think that an application which only downloads parts of the blockchain history is likely of little use, due to the potential for abuse of trust.