Ralph Ketcham’s book Presidents Above Party shows that the first six presidents understood the veto power that way and only used it that way. The classic example is James Madison’s Bonus Bill Veto, which was a veto of a bill he had repeatedly asked Congress to pass. I describe that in James Madison and the Making of America.
As Ketcham notes, the change came with Andrew Jackson’s Bank Bill Veto. In the message explaining the veto, Jackson referred not only to constitutional objections, but to political and sociological ones. Since then, presidents have used the veto power as a means of insinuating themselves into the legislative process. Congress has funded an increasingly large presidential staff, which helps the president in his legislative functions.
I agree with Washington and Madison about these matters, but it’s hard to imagine a president eschewing the power the Executive Branch has accumulated since Jackson’s day.