The time-turner was also under strict control of the Ministry- didn't Prof McGonagall have to give special reasons so that Hermione could use it? I can't see the Ministry granting usage of it to get back Sirius, who is- in their eyes- an escaped and dangerous dark wizard. That would lmean the only option would be to steal the device.

We'll have to wait and see what JK's grand plan for the death storyline is. I'm sure it serves a greater purpose than is seen in this book.