Ferrari tried your suggestion for Australia, and it didn't work. They were kind of saved by the first safety car.
Well, I think the Ferrari strategy failed because they over-estimated how long they could stay out on the super-softs. I think they'd probably fueled for 15 laps but then found their super-softs degrading earlier than expected. I guess they were reluctant to compromise their fuel strategy and didn't bring their cars in early enough for a tyre change.
On the flipside, Williams failed by using the opposite strategy. Rosberg's third stint was a disaster as he destroyed his tyres setting the fastest lap late on.