This is not a coincidence or oversight, we chose to charge per line. After all, ‘the’ is a word, but so is ‘antidisestablishmentarianism’… And the number of words a page contains varies depending on the font and layout of a text.
So it is difficult to charge objectively per page or per word. Though objectivity is necessary to put together a proper quote for your translation. This is why Ad Verbum translation agency charges per line. A ‘line’ consists of 55 characters, including spaces.