I don't see the point in storing a lot of private keys simply because deterministic key derivation exists. You only store the seed for that KDF and then you can always derive the same exact 1000 private keys in a second whenever you want.
I can think of a reason: convenience! It's very easy to take 1 private key from cold storage, and use it to spend funds. You might even be willing to enter it into a hot wallet.
But if you have one seed that gives access to all your private keys, you'll need a cold storage setup just to spend funds from one key.
I could see that be useful with a handful of private keys but 1000 still doesn't make sense to me. If that many keys are being used buying a hardware wallet or setting up a cold storage (DIY) makes a lot more sense than having a "book" of private keys to spend from.