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.
Read inside the box. If you install 14 AWG conductors to the new box, instead of 12 AWG conductors. You'd need at least a 22 cu.in. Box, or a 3" x 2" x 3 1/2" device box.
- 8 for current carrying conductors.
- 1 for grounding conductors.
- 2 for device fill.
11 total, times 2.00 cu.in. for 14 AWG conductors = 22 cu.in.
However, since you're using 12 AWG, the calculation looks like this...
- 6 for 14 AWG conductors x 2.00 cu.in. (12 cu.in).
- 2 for 12 AWG conductors x 2.25 cu.in. (4.5 cu.in).
- 1 for grounding conductors x 2.25 cu. in. (2.25 cu.in.).
- 2 for device fill x 2.25 cu.in. (4.5 cu.in.).
Total = 23.25 cu.in.
For more information on box fill, check out this answer
As for connecting the new wire. There should be no problem attaching it to the receptacle. However, since you're using 12 AWG conductors, you'll have to use the screw terminals.
If you want to do pigtails, you can. I know some guys don't like the backstab connections, so if you want to avoid using them you can do pigtails. Ideal 76B® Red Wire-nut® Wire Connectors are rated for 2 to 5 #14 conductors, but check with the manufacturer of the connectors you're using. Again, if you're going to do this, you'll want to use #14 conductors instead of the #12 you've installed.
Best Answer
The receptacle manufacturer should document how many wires can be put where. In general, if there are screws, you can use at most one wire per screw. For quickwire/backwire holes, you can only use one wire per hole, and further, that one wire can only be 14 gauge. Previously, 12 and 14 gauge were allowed for quickwiring, but not any more. The only kind of receptacle where you can directly attach a whole bunch of wires are those where the screws tighten down a bar onto another bar. Then, you stick stripped wires between the two bars and tighten the top one down to clamp them between the two bars; you can run quite a few through there.
Another limiting factor is box sizes. Boxes have a fixed wiring volume, and there are rules for working out the minimum volume box needed to accommodate a given number of wires, devices, and clamps. Assuming you're working with 14 AWG grounded cable, I'd expect the box to accommodate 4 hot + 4 neutral + 1 device + ground wires, so 10 wire volumes, and 14 AWG is 2 cubic inches per wire, so you'd need a 20 cubic inch box. That's a bit on the large size for a box holding a single receptacle, but there are boxes and box configurations (box + mud ring) that would accommodate that many wires, so it's not unreasonable.
As for wiring everything together, you should pigtail everything and then hook up the pigtails to the receptacle. The pigtail presents a single wire for slipping under the screw terminal. Remember to wind the J-hook you'll slip around the screw in the direction that you'll turn the screw to tighten it, so down on the left side and up on the right side.