“Last call”? No idea.
I think the teardrop after you cross over the airport is extremely useful for safety. Your turn to the right, for a left downwind, gives you a comprehensive view of all the departing traffic & those staying in the pattern—departure, crosswind, & downwind—as you descend to pattern altitude.
If you did a non-standard turn to the left after you cross the airport, you’d be turning your back to the traffic in the pattern & not give up a lot of situational awareness just when you need it the most.
After all. You’ve got to get down to pattern altitude & reverse course into the pattern somehow.