1) The private key is stored on the secure element on the Nano. It does not leave the device.
2) Ledger can go out of business tomorrow, shut their doors, shut down their systems, get hacked - all of the above. Your crypto is safe.
3) if you lose your Nano, you can restore access to your funds using any BIP39 compliant wallet and your seed.
The benefits of a Ledger over paper?
1) if someone finds or steals my ledger, they need my pin to do anything with it. If they have my paper wallet, I'm screwed.
2) If there's a fire or other disaster, I can recover my ledger using the seed to any number of hard or soft wallets of my choosing. My paper wallet is gone forever.
3) Since my private key is never revealed even to me and remains on the secure element of the device, it is not possible for a hacker to gain access to my funds if my PC or network is compromised. All I have to do is enter my paper wallet into a soft wallet on my PC once and that paper wallet is no longer secure.
You would be correct, however, in pointing out the Achilles heel of the Ledger is the seed. This is mitigated, however, as the seed is generated offline, so it is at the very least as secure as a knowledgeable person setting up a paper wallet. You can further secure the seed using something like a cryptosteel and dropping it in a safe deposit box. Now you have access to your crypto via a secured protected device (Nano) and have recoverability in the event of loss theft, damage, or Ledger going out of business (BIP39 seed on cryptosteel).