I started thinking about this last night and it seems every year it takes 2 or 3 weeks before we start seeing great performances. I think a lot of it has to do with getting used to performing on the stage, before a crowd, and with the pressure of knowing millions of people are watching and going to vote. Not to mention, getting used to the weekly routine, the band, and what help is available to help. I imagine for almost all of them, their head is still spinning as they try to adjust to life on AI and learn all the little things they need to know.
And I'm going to disagree with you. I don't miss Paula at all. Paula rarely (maybe twice a year) actually judged, rather most of the time she acted simply as a cheerleader.
The bickering and "chemistry" between Paula and Simon was manufactured -- you can tell they are friends off screen and that most of what happened between them on camera was scripted. I knew last night when I saw the seating of the judges exactly what they were doing, even before it was pointed out. They are putting Kara next to Simon so they can have a similar type of bickering/chemistry between Kara and Simon as they did with Paula, though it will be a bit different to fit Kara's personality.
As for the little clip at the beginning, I found it funny. Mostly because guys don't ever seem to care if a woman is gay -- guys always seem to think they can "cure" women of lesbianism. In fact, often guys will try even harder when they learn a woman is lesbian because of the "challenge".