At risk of egging moogy in to a long useless discussion... The term ace is not really defined obviously.
Being what people would consider an "ace" is more about ability than durability. Way more. Sure, you want good pitchers to log more innings. Obviously. An ace caliber starting pitcher who is also dependable is the most valued commodity in all of baseball because those guys (Felix, Kershaw, Verlander) are so rare and hence they get the mega bucks. Deservedly.
The question for a GM can become what do you want in your rotation - an ace quality starter like Strasburg who has been breaking down a lot - who should pitch really well when there but might give you 80IP or 180IP. Or do you want a reliable mid rotation starter who's a workhorse who never misses time. Both ace talent and dependability have value. You might not want 5 Strasburgs in the rotation if the backups are all terrible. And no one can afford 5 Kershaws. So you mix and match and you need depth, more so if you have fragile guys like Morrow.