Do the validators need information from the blockchain to produce blocks, or is it enough just to store a few recent blocks? What is the incentive to use large amounts of storage to store the complete ledger (or when sharded, store the full shard)?
It's not just in Casper, it's in every consensus protocol out there (to my knowlodge). Full non-miner nodes does not benefit economically from the veriffication process, but if you want to validate your transactions by yourself (you're a big user and you want to be more secure about your transactions), you can run a full node.
this link provides more explanation
Have a nice day :D
EIP 908: Reward clients for a sustainable network