Any wire connector can fail. Screws can loosen with vibration, stress, corrosion, temperature fluctuations, and so on. Push-in (or stab-in) connections can fail for the same reasons. Crimp and pin connections, friction lock, and even soldered joints can fail.
The real question is: what's the most effective wire connection given the operating conditions, parts and installation cost, lifetime expectancy, use case, and so on.
For example, where I work (we manufacture large electric signs), we use all manner of connection methods, and they vary based on these factors. One such factor is serviceability. If a connection is expected to be rugged and reliable but disconnected for safety reasons, we may use screw terminal blocks (which only accept straight wire) or friction lock (which requires use of a screwdriver to release, similar to the push-in connectors on outlets and switches).
Outlets shouldn't require frequent service nor replacement, nor should experience extreme vibration. They also won't (usually) have wide temperature swings, which leaves the stress from normal usage (connecting and disconnecting plugs) which can wiggle things loose over time.
A well-made outlet can have quite good push-in connectors; by "good" I mean they hold solidly for years and aren't likely to fail with normal use. However it can be difficult to tell during installation whether the inserted wire has made good contact or not. Also if one happens to be faulty, it may accept the wire but provide little feedback that the locking mechanism is less than optimal. Pulling on the wire after installation is one way to tell, but if you're using the push-in connectors, are you spending the extra time to do the pull test? Probably not. Screw terminals are easy to visually inspect and determine if solid contact is being made and that the wire is firmly held by the screw or plate.
So while push-in or friction lock connectors can be quick and useful in certain applications (with appropriate confirmation of operation), I recommend wrapping wire around the screw terminals for the most durable connection that's easily verifiable. Usage and vibration can still loosen the screw, and in such case the wire hook will be less likely to separate from the outlet than a straight wire. In all cases where the screw comes loose, however, arc fault can occur, causing problems.
Provided you follow the same precautions as a NM run parallel to and/or through frame members, such as keeping it a minimum of 2" from the edge of the member, and secure the cable properly to the deck and walls (again, treat it like NM), this is A-OK. (You'll want to use grommets if you go through metal joists, but again, that's the same as running NM through a steel stud.)
You'll need to put in a surface-mount box for your new fixture, of course, unless it provides its own wiring space (i.e. is volume marked).
Best Answer
Yes. Those misfeatures are actually features. They are designed to help you keep the wire captive and in the right place.
First, there is a hook designed to hook the existing wire (i.e. the short on the right side) to help you make the J-hook more than 180 degrees to make it captive on the screw. The idea is now, you don't need to use a needle nose pliers to make that final over-180 bend. This won't make any sense if you're making the J-hook too short to benefit from this feature.
Second, it helps keep the wires "trapped" under the screw, so you don't have it slip out from under and fail to notice it if you are working quickly.
This "Trapping" is especially helpful when using stranded wire, which tends to squish around and fray when tightened. I use a lot of stranded wire, and those things are a godsend. As the screw gets nearer to bottom, these gates will fully entrap the wire so it can't frizz out of the hole. You still need to give the strands a really sincere twist, but it helps.