I worked my way through school as an electrician - and have handled many wire nuts (also wing-nuts, fruits and nuts, and nuts of all stripes) in my time. They work - but their effectiveness is directly related to the wrist and finger strength of the user and/or the prep prior to use.
For solid wire, twist the wire together first making a good mechanical grab, clip square, then use the nut to preserve that grab against movement. And, "Dying Strain" are the watchwords when installing the nut.
For stranded wire, twist the strands together first, and twist until the entire wire starts to twist, and much strain applied.
For stranded-to-solid, extend the stranded about 1/8" beyond the solid - and as above thereafter.
The correct size is critical.
The final connection should be as strong as/stronger than the weakest wire in the chain, uncut.