to over-simplify: dried yeast are "freeze-dried" at the height of health. they have all the nutrients they needs, including sterols, so no need to provide sterols when they come back to life. O2 is the easiest and most common way for for yeast to make sterols. since dry yeast already has its required sterols, O2 is not needed. if the yeast don't consume the O2, other critters might... usually yeast is quick to eat up all available O2 thus starving off the invaders. if the yeast don't need it, the critters will use it for their own nefarious purposes.
using sugar to rehydrate is bad for two reasons. one, as previously mentioned, it can compromise yeast's ability to consume more complex sugars like maltose. second, when dried yeast are rehydrating themselves they suck in everything, indiscriminately. they can't control what is entering their bodies. rebuilding yourself with water = good, building your body with sugar = bad. it's water that was removed when they were mummified, so it's water that needs to be added back as they return to life.