so the most modern safety feature requires me to write it down and store in a safe place?

1. The Recovery Key is not used to protect your iPhone at all. It's used to protect your Apple ID and access to it.
2. Yes, the recovery key is a one time thing, and must be kept safe. If you forget your Apple ID password, and lose your recovery key, you may not be able to regain access to your account. You can store it in a secure digital location you can access without needing your Apple ID. It does not need to be written down on an actual piece of paper.
3. Why is writing down something bad? The most secure way to store something is still as a physical copy in a secure location. Not sure why it's bad to write something down. In the event you forget your password, and need to regain access to your account, you will need the recovery key. It makes it harder for anyone that is not you too regain access, as they will need that particular code which is not stored anywhere expect wherever you store it.

Access to your iPhone is not restricted or limited by generating a recovery key.