I'm on my fourth character. I reached the point where Delphine wants me to prove I'm dragonborn.
I did something I didn't do for my previous 3 characters - I refused and told her to stop wasting my time. She was clearly quite irate, but didn't try to stop me from leaving.

Here's the kicker:
Since then, not only have I not had a single dragon encounter, but they seem to have disappeared. They're not circling in the skies, I never hear them roaring in the distance - it's as if they've VANISHED.

Is this a bug, or is it a happy coincidence?

How long has it been? Did you try going to a dragon lair?

Depends. Have you been fast travelling?
I daresay it's just a coincidence, though.