"I really don't understand how people are have problems with their analog sticks"
Well then, I guess there are some things that are too much for you to comprehend.
One of my analog sticks has some wear. Still very happy with the PS4.
It is hard for me to get comfortable with the analog stick, for some reason it leaves mark on my thumbs. I find it too small, hoped for a bigger surface area. Also it needs bigger battery, the battery is just awful.
The battery is awful! I couldn't imagine only having one controller! This may seem off topic but it actually applies to the bad battery life. they need to get rid of the notification that pops up on screen when your controller turns off. This is really annoying when viewing a movie. I would just leave the controller on, but the length of a movie will just about run the battery completely out.