This is a really good question so I'll try to give you a good answer.
The rationale for adding the D'Arce from side control bottom is primarily about balancing gameplay. We wanted to provide a submission from as many positions as possible as providing both players options allows for more variation in strategy. D'Arce control from bottom side control is often one of the first submissions taught from that position in BJJ and even though it is not necessarily a high percentage submission it is often used to get your opponent to do something differently and open up an opportunity to escape. We decided it was the best choice to fill out that spot in our game for the same reason.
You are correct that it is more commonly applied from the other positions you listed, however there is a cost to adding a submission to any position and those positions were already covered by other submissions. I still recall the conversations we had around sprawl and adding the D'Arce there, however we felt that the Japanese and Peruvian neckties deserved some love and were uniquely made for sprawl.
Regards TOS