Follow-up questions:
If there becomes 100 trillion wallets in use, do you think finding a wallet with a balance will become common? Is the current private key secure enough to last 10,000+ years?
Is there a way to scale up the security of the generated private keys somehow if needed someday?
If you have a huge volume the just store it on a flask drive or external hard drive that way the hacker will no longer have an access to your bitcoin since it is not connected online. There are many ways on how to store your bitcoins especially for big time holders. If you are just doing your research then you can find many alternatives on how to avoid hacking and some of it are on this forum.
I don't think this is accurate. If there's anything "in your wallet" then that means the address has already been entered into the blockchain and is now a matter of public record, so if there were a way to hack someone's private key from their public address it would be easy to find. Even if you have an "empty wallet," which is kind of a nebulous term since at that point it's just a generated key, the question the OP was asking is whether or not someone could hack or randomly generate a duplicate key which corresponds to someone else's wallet - the answer is yes, whether the key has ever been used or not. As other people have said, though, the chance is ridiculously small. It would take far more than the $100 billion market cap of all cryptocurrencies to even come close to the computing power necessary to generate, test and transfer out large amounts of bitcoin from other people's randomly-generated wallets. At that point we'd be better off devoting a supercomputer to spend 7 million years coming up with the Answer to Life, the Universe and Everything... though we'd probably come up with 42.
As far as security for keeping your bitcoin personally safe, yeah, keeping your private keys in an encrypted paper wallet that's been generated on a new, freshly-formatted computer with no network connections and then putting the paper wallets in a lead box and storing them in an underground bunker is probably safe enough. The hacks that I've read about weren't instances of people's wallets actually being hacked, but of the private keys being found when their PC's security was compromised.