> If the sending server doesn't do DKIM, it's fundamentally broken,
No, it just won't get very good deliverability, because everything it talks to is now fundamentally broken.
DKIM shouldn't exist. It was a bad idea from day one.
It adds very little real anti-spam value over SPF, but the worse part is exactly the model you describe. DKIM was a largely undiscussed, back-door change to the attributability and repudiability of email, and at the same time the two-tiered model it created is far, far less effective or usable than just end-to-end signing messages at the MUA.