In 1968, Burch worked in the campaign to return Goldwater to the US Senate for the seat vacated by retiring Democrat Carl Hayden.

Because of his presidential nomination, Goldwater gave up his Senate seat but returned to the upper chamber after a four-year absence and served another eighteen years.

Under Burch, a study was conducted to determine whether one company should be allowed to own a daily newspaper and a television station in the same city.

In 1975, shortly after Burch left the commission, the FCC unanimously prohibited the formation of new combinations of newspapers and broadcasting stations but allowed existing ones to continue.

In 1980, Burch was chief of staff on the Republican vice presidential campaign of George H. W. Bush, the running mate of Ronald Reagan.