Angling the pin off axis allows the bass to either increase or decrease a certain amount of "spin". In my experience with all sizes of basses and people, I have found that those that do not keep contact of the bass with their belly or waist area, lose control of the bass and it spins out, toward the left. Some compensate with angling the pin toward the G string, as you put it, to make that spin out less strong. To me it generally shows a lack of understanding of the balance that is required between contact with the waist and thumb and floor. When in thumb positions, especially high on the E or A strings, many suffer from the spin out to the left and so they squeeze their body and arm elbow and such around the bass. This fights the whole reason for having a bent endpin in the first place: to allow natural weight of the arms to play the bass, without a lot of muscling going on. So, the easy remedy is to keep your back straight and always keep contact of the bass with your belly or waist area. It seems more challenging with a bigger heavier bass. So sometimes angling the pin leftward is the only way to alleviate that spin feeling. In 90 per cent of cases I have encountered, it is more about stance and holding the bass than it is about the angles of the pin. Starting from exact center, then 44 to 45 degrees back so that the end of the pin contacts the floor at least in line with the back of the bass or two to four inches beyond the back, for most 3/4 size (standard "full size") basses, seems to work well for the balance of the instrument at the "proper" playing angles for the arms. If the player is short and the bass is big, or the player is quite tall and the overall angle toward the player isn't great enough, then one remedy to the spin problem is this angle off axis toward the G string. Remember there are always three angles to deal with, and they all have an effect on each other. Then, trying to force old techniques of stance and playing in general onto the new stance often causes one to search for feelings of familiarity. One must be open to the new technique and let it evolve into one's playing. It took me two full years to even get comfortable with the pin and another ten years to feel mastery. Life and virtuosity are about change!
Hope this helps a bit.
Patrick