The answer is similar to the ones to earlier questions: It is mainly practicality in full-contact sparring vs. ideal technique.
Theoretically, fully opening the hip by more pronounced foot rotation offers you two things: Firstly, you can do a powerful roundhouse kick just as well, with the very same opening, which makes you less readable. Secondly, it is supposed to allow for slightly more stability against forces in that direction and thus help against toppling backwards.
Practically, this is slightly slower and needs immense hip flexibility and strength in order to not actually weaken the kick due to structural instability. You can actually see how the karate guy's structure is compromised in the picture as he only stands on the ball of the foot to make up for his lack of hip strength/flexibility.