A couple of points:
In general, children, especially really young children are veritable factories of germs. I thought everybody knew this? Children are practically packed full to the brim with germs, because they are children. They don't give 2 shits about hygenie because they don't have the maturity to stop and think about it. What's your excuse?
Anecdotal evidence is the weakest kind of evidence. Indeed, calling it "evidence" at all could be called misleading.
I personally think that people who don't wash their hands have no place in polite society.
You have dry hands? Well great news! There is this newfangled invention called "liquid hand soap" that is not only specifically made for washing hands, it also has none of the harsh drying effect that bar soap does. Hell, you can even get it in a moisturizing version!
You are absolutely right that, in general soap and water is more effective than hand sanitizer. It is intended to be used in situations where you can't wash your hands, or as a complement to washing your hands when they have touched something particularly dirty. It does have that nasty drying of the hands side effect, but again it's meant to be used sparingly.
Lastly a big part of this pandemic that people can't seem to wrap their heads around is this- many of these precautions are intended to protect other people more so than yourself. You do remember that other people exist right, not just you?