That's the basic idea for using ale yeast instead of wine or champagne.
The rub is that if you go past 1.070 or so, you will wash out a lot of the apple taste. And even at 9%, most ale yeast can struggle along for a while. But they are a lot easier to stop with cold crashing at this point
traditional cider houses use nutrient reduction so that the yeast runs out of nitrogen before it runs out of sugar. This is tricky and requires a consistent source of good juice. pasteurizing is a lot more reliable and easier. cold crashing is easier still if you have kegs, although it takes a bit of practice to get down.