There is a term for this.. "priming" or "flushing the muscle" or flushing technique..
It is a workout technique. For example let's say your doing a barbell bench press that works chest, shoulders, Tris.. and an overhead press that works shoulders along with 3 chest moves, 2 Tri moves, and a shoulder move. Working out all the chest moves first(or Tris, etc..) is beneficial because you're "flushing" the muscle with nutrient rich blood, helping to recover and give your muscles energy. After moving on to chest exercise 2.. your muscles still are flushed so they are alert and full of energy so to speak, and you can hop right into an exercise with less fatigue. Flushing the muscle and working all 3 chest moves first help cause healthy muscle micro tears and flush the muscle with blood, really aiding it to grow. It will also make you a bit stronger as there is nutrient rich blood flushing your muscle. Afterwards your chest will be VERY sore and swollen.
How does it reduce fatigue? Think about doing a bench press, then flyes, then a trip and a shoulder move.. then do an incline dumbbell press..your chest muscles at this point are not "flushed", and will have less energy. They will have also already started healing so you may start feeling sore which again leads to fatigue or an incomplete set. This is not an issue usually with total body workouts as each muscle is getting hit as a result of a conpund move, and really only gets hit once per workout. Working out different muscle groups at different ends of the body back and forth with enough reps can cause lactic acid buildup which is another pro for using flushing instead. You're chest might have buildup or burn but once you finish you finish. Do your toughest exercises first in terms of difficulty then your easy exercises. Workout your weakest muscles first as they get the most energy. Nowadays fitness experts are experimenting with blood restriction training which essentially flushes the muscles as well but keeps the blood isolated to the muscle group and flushes it even more. I have not done much research on blood restriction training so I prefer the typical flushing method.
Typically you'll do all your compound barbell exercises.. so in the example above you'll start by doing a bench press or overhead press first, followed by the other since these drain your energy. Then workout your muscle groups in order from weakest to strongest muscle groups and then in order of decreasing difficulty. I won't lie, doing your musle groups in order will make your last set hell, so save the easy isolation exercises or machine exercises for last.
There's not really a con, it's just a method of working out. Schwarzenegger was actually a huge fan of working out opposing muscle groups in supersets to remain symmetrical and to aid in hypertrophy. He still lined up the antagonist groups with muscles in order to flush them however.
There's no negative for this method. However it might interfere if your doing other methods such as circuit training, pre-exhaustion sets, burn-out sets, or others.