iMessage also syncs to iCloud unencrypted by default[2].
[1] Depends on you paying for iCloud storage, so that you have space for a full phone backup to occur.
[2] Might be "free" with "iMessage in iCloud", an option to enable separately.
Not true. You must choose to enable it or not when you set up new phone. On mine it does not back up
Also, backups have nothing to do with the messages being end-to-end encrypted. Like if you don't use a passcode on the phone, the messages are still encrypted.