I use 'em in special situations--
1. I open up a box for a switch or outlet replacement, and the whole thing is so full of debris (paper filler, plaster, dust) that I feel obligated to clean it up. Usually one or more of the conductors is verrrry short.
The push-in connectors are compact enough that the box is easier to get back together, and being able to stab-in the wire can really save the day.
2. Any old work situation where the wire is way short, basically impossible to get a wire nut onto.
3. New construction where the rocker's router has trimmed one or more conductors short.
Those of you who don't like 'em, have you made a splice with one and tried to pull it apart? I have, and have found the clamping action strong and irreversible. Keep in mind that a lot of guys though wire nuts were bogus, thought that a properly wrapped and soldered splice was the only was to go...