Is it important to have an unencrypted backup of the private key? Am I correct that in not having our private keys written in paper or otherwise backed up we are implicitly trusting the wallet developers to keep publishing wallet versions that are capable of reading and deciphering our password-phrase? Nobody else can decypher that phrase and give us access to the bitcoins, correct?

I recently had a bad experience with Mycellium wallet: i lost my Android mobile and the backup of my wallet was in a 1-year-old format (encrypted private key in paper, QR format) that the new desktop app, amazingly, would not recognise. In the meanwhile, I had moved to iPhone, where no Mycelium was available. Eventually i solved the issue by installing Mycelium in a friend's Android. Fortunately, the Android version did recognize the old encryption after scanning the QR with the camera, so I could send the money to another wallet. But this made me realise that we absolutely rely on the developers if we do not keep the private keys written somewhere, unencrypted.

In other words: What happens if a wallet app is discontinued and we find ourselves in 2020 with no way to install that old wallet in the 2020 standard devices?

Or am i missing something here?

Thanks in advance
It is important to be able to recover your private keys using only tools you fully control. That protects you against failure of infrastructure you would otherwise need to transfer your funds. There are lots of stories of corrupted backups, unreadable backups, and backups that didn't actually include the private keys.

Storing your private keys unencrypted on paper is one way of doing this. They can also be stored electronically in encrypted form, so long as you have reliable access to the encryption key and decryption tool.