> On a good wire nut connection the wire nut is just insulating the bundle and if it falls off the bundle is still secure.

The problem is, a good wire nut is impossible to distinguish from a bad wire nut. A transparent Wago (or its clones) are virtually foolproof to install and to inspect.

No. If you use a good wire nut (i.e. use a good brand, have experience, and never reuse a wire nut), the nut itself makes the electrical connection. A good wire nut application will never fall off. If it does, you didn't attach it right. I concede this is a function of experience and it's not foolproof.

All that having been said, I still pre-twist because it helps keep the wires together which makes it easier to put the nut on in the first place -- especially if you're connecting more than two wires.

Edit: One point I left out is that if you don't pre-twist, correct attachment means you should put the nut on with enough tension that the nut itself causes the wires to twist together. This hurts your fingers if you do it all day, so using a wire nut twisting tool is recommended.

I knew about that, actually. It's way too big still for some uses, and I'm guessing won't deal well with anything that repeatedly lightly pulls on the wire (e.g. a trunk hinge). But for some other cases it's great.