The benefit is that you can access your bitcoin wallet from anywhere.
Blockchain.info is designed so that the private keys are stored in the client's browser and never make it to the server. Some people think this is more secure because blockchain.info never sees the private key, but now the private keys live in your browser's localStorage. Its just as likely to get hacked there is it is to get hacked on blockchain.info
There are some things that sound interesting to me... you get most of the advantages of both running a full node and an SPV or web client (full blockchain validation but lightweight on your client devices).
I'm not sure what you mean with regards to blockchain.info though. Keys are stored encrypted both on their server and in localStorage (but not in RAM). If you enable two factor auth, even the encrypted keys are no longer stored in localStorage by default. Not that it's perfect, in particular their default key stretching is pretty minimal.
Also I wonder how long a $5/mo. DigitalOcean VPS with it's 512M of RAM would take to do the initial blockchain indexing.... you could always beef it up during the initial indexing I suppose.