DNA in blood of birds.

I have just learned that the red blood cells of birds contain DNA.

This suggests to me that the blood of all vertebrates including turtles,
amphibians, fish, sharks etc may include DNA.

Is this correct?

The only significant advantage of not having DNA in red blood cells I
can think of is size and therefore the ability to reach more locations
through smaller vessels.

No doubt there are other advantages I have not seen. Suggestions?

Friar Broccoli (Robert Keith Elias), Quebec Canada
I consider ALL arguments in support of my views