MP sounds like you got it figured out. Each connector is designed to connect all of the neutrals, or all the hots or the ground wires. One connector for each of them you cannot mix hot and neutrals in the same connector. Take care Ron at firstname.lastname@example.org
For 110-120 v cables, it is absolutely, 100% against every code from every country and state of which I'm aware and has been for over 100 years when they first came out with any codes anywhere. Doing so is probably close to the top of the list of things that cause house fires which are, if given an affirmative answer to your question by definition, within walls so any such incident will likely be out-of-control by the time it's discovered. The only POSSIBLE exception that I can think of is for no/low voltage wires and cables like hardwired phones, internet cables, antenna wire, doorbell wire, etc. I don't have the time to research that topic and so I'm not 100% certain whether it's prohibited or not for no/low voltage wires. But it's NEVER a good idea for any type of wire simply because without access it's much more difficult to access future problems or make future upgrades.
Perhaps it's possible to push in such wires into the device without bending or breaking any of the individual strands, and to get a great connection, but you would have a much easier time and be much more secure that it's a strong connection, if you solder/tin the wire first.
These are designed as "easy" push on wire nuts! For 110v household type wiring, you need three of these per connection, 1 for hot wires, 1 for neutral wires, and 1 for ground wires. They have the same functionality as butt connectors or wire nuts.