The end zones are not "the field". You don't score 6 points on the field, you score points in the endzone. If you are on the field, break the first down marker plane, but you bring the ball back, you don't get a 1st down; the endzone, the tip of the ball breaks the plane with possession, you get 6 points, even if you bring the ball back out. There are other differences, but the point is, the endzones are not "anywhere else on the field".
And again, if the offense is too inept to hold on to the ball before they cross the line, they don't deserve to get the ball back.