I've learned that it takes 3 coats...6" 8" and 12" skims the rest of bare dry wall. You end up skimming all bare dry wall. If you paint any bare dry wall don't it swell up and need sanding, mud and paint again? Isn't it: 6" knife for tape, 8" knife goes out from there, then 12" skims the rest of bare dry wall. ? With sanding in between.
You do not need to have joint compound or skim coating spread over the whole wall before painting. The correct way is to use the compound and skim coating plus any needed sanding to cover seams, nails/screws and other types of repairs. Then you prep the whole wall using an appropriate sealer coat or primer paint. Lastly you come with your final paint coats.