Why not?

In RC4 the full 2048 bit are needed for the crypto process. Storing less than 2048 bit per key would be a fatal mistake, since the data to encrypt/decrypt decides which parts of the 2048 bit are used at what time. Storing only the 40 bit password and doing a permutation later is pointless, since you can calculate the next password always just by incrementing a 40 bit variable by 1, which is of course faster than reading the next 40 bit key from a hard drive.

Using binary search instead of linear is no (usefull) option, since I just highlighted that hard drives and even RAM are far too slow.