You are mixing concepts a little here.
Height and padding have no correlation in most cases. The problem with a fixed height was that you were applying it to fix problems rather than sorting out why things weren’t as you expected. e.g you had not contained floats and had forgotten about margins increasing the space elements take up.
A wrapper will not need a specific height if you have taken care of the elements inside properly.
Of course things like iframes and images need height but any containers that contain text or fluid content should not be a fixed height. Sometimes it may be appropriate to use height if you need to match something explicitly and when there is no danger of that height causing a problem.
Don’t latch on to one concept and think it applies to everything because the methods you use depend heavily on the task on hand.
There is no one size fits all in css which is why some people struggle with it because although some methods may appear to work they may be the wrong methods for the job in hand