The Burke benchmark pulled Constellation toward a destroyer

Did the Constellation-class frigate become a destroyer because it was expected to match the Arleigh Burke?

To an extent, yes; the Burke's broad competence makes smaller US warships grow toward it or become unusually specialized to justify themselves.

The Constellation class drifted toward a small destroyer because it was repeatedly judged against the Arleigh Burke. The Burke provides a strong solution to many missions, so proposed alternatives are either expanded toward its capability or pushed to extremes to justify their existence. That benchmark pressure makes a disciplined frigate requirement difficult to hold. A successful incumbent class can distort the design space around it.