When these first came out, they had a tendency to fail at the hinges, especially in the wind. While the leading makes have probably dealt with this to some extent, not all makes will have. And this can mean more failures than you carry spare hinges, in one go. A permanent repair can be easy or hard depending on the hinge/clip design,and a field splint is likely be harder for a failure at a joint than in the middle of a section.
For the smaller ones, not being able to split the weight between two people in a disadvantage. Even for tents that would only be used for car camping, having all the weight and bulk in one lump can be awkward especially in a small car. They also tend to be bulkier to pack than an equivalent conventional tent.
When pitching in even a light wind, putting in 2--3 pegs on the upwind side before the tent has any height can be a huge help, especially if you're on your own. If the poles automatically lock together when you spread the fabric, this will be harder. Against that you can offset the extra weight of the poles, so you should be able to find your own workaround.
The clips used to be annoying to find and undo when taking the tent down, so the total up+down time wasn't necessarily much shorter unless you were tall enough to reach the high clips first. Again this may have improved.
Having said all that, it might sound like I'm against self-erecting tents. We plan to give them a good look when buying our next car-camping family tent, as being able to put the tent up single handed is a big deal, and we drive a windbreak and plan to camp in decent weather.
If you arrive home with a wet tent, being able to hang it up without poles is useful.