An angled flight deck resolves many problems identified during WWII with carrier combat and flight operations (in addition to some of the other issues related to jet aircraft).
The first relates to the importance of not having a crash landing stop flight operations (or wreck staged/landed planes). For example, straight deck carriers often recovered planes in a fashion like this (images from Wikipedia, the USS Saratoga):
Notice the plane landing has a short distance to actually land/stop.
It is important to realize the implications of a crashed landing or an overlanding. A plane landing at this way, if it somehow jumped the barrier/missed/overshot is going to crash through many parked/staged planes. Clearing a flight deck, even with multiple elevators, is not instantaneous.
Next, let's consider the takeoff process. Again, look how many planes are staged on the flight deck:
This sort of operation was typical in the era before and during World War Two.
It's important to realize that most carrier configurations looked more like the ones here than what we think of when we think of a supercarrier when the angled flight decks were introduced. The experiences of those running WWII flight operations and the lessons learned drove the implementation of angled flight decks.
Imagine too if a plane returning to the ship suffers damages during landing or crashes. Given how the flight operations worked, this would prevent the ship from doing anything until the plane was dumped overboard/pushed out of the way. In a combat situation, precious minutes could mean the difference between a CAP being launched -- or no planes being launched.
Additionally, having two "runways" means multiple planes can be launched simultaneously. You get nearly twice as many launches per minute when having two runways.
The USN was already experimenting with multiple launch points with a hangar deck catapult with the Essex class:
While not wildly successful, it shows the USN was already interested in having multiple launch points for planes (don't try landing through this area!). These were all removed eventually during WWII but the need is indicated through their initial installation - six Essex carriers had hangar deck catapults installed.
Again, this indicates that there was a compelling problem to be solved with a straight flight deck and single launch/failure point.
Related to the increase in plane weights, having a longer "landing" zone allows heavier planes to actually accelerate upon landing in order to have enough airspeed to abort if needed. With either configuration as shown here, you would never want to be accelerating on landing if not required to prevent stalling - if you did you are simply increasing the risk of crashing into the other parked planes. Especially as plane weights increased and speeds increased, the risk of overshooting the barriers increased.
Another advantage is the increased ability for elevators to access the hangar deck. With a straight flight deck, you only can really have elevators that take away from your usable space. While the Essex class started this trend, having their elevators slightly sticking out from the ship, look at where the elevators were located in your image - they are completely out of the way of both flight decks. This is another advantage of the angled flight deck, because it means you can operate the elevators and use them to stage planes without significantly affecting flight operations. A straight flight deck has minimal ability for this.
Last for this mini-book, having two "flight decks" means that in a combat situation, a single bomb doesn't put your ship out of action. Many US carriers were put out of action temporarily from single hits to their flight deck. Having two "runways" means that you build in some safety in that you can use your ship to launch or recover aircraft even if you take damage (again, keep in mind that during these conversions WWII was fresh in the minds of designers/naval officers).