This question was originally posted on Stack Overflow by the following link: https://stackoverflow.com/questions/50585255/how-to-prevent-rectified-images-to-be-cropped-in-opencv
Unfortunately, most probably due to my high activity in content moderation, it got several "revenge downvotes" and it was automatically deleted by the system. This question got around 500 views in 1 year, so I assume other people also encounter this issue, hence I decided to save a copy here.
While there is still no answer to the problem of cropping, I think my attempt to solve it which is presented in an edit to the question will be helpful for future readers.
Let's take the following pair of consequent aerial images and do the image rectification (code below):