Wow that is a lot! I will admit I do NOT wash my hands nearly that much. I was not raised with handwashing being something that we did, my mom never had us wash our hands really ever, so it is not ingrained in my day. I have been trying to get better about it but it is surprisingly hard to rememberu. I do wash a lot before, during and after food prep especially if it inolves meat or eggs. I usually don't wash after pees but I do after poos mine or DDs. I don't make DD wash her hands after she goes potty, she is not wiping herself yet, so she doesn't touch anything. I do wash after using a public restroom and I try to remember to wash before lunch and have DD wash too but I would say I forget about 50% of the time. Never do it before breakfast and tend to never do it before snacks either. I don't really stress about washing after we have been out and hardly ever use sanitizer only if we are going on vacation soon or something. Otherwise I'll wash them if they "feel" icky. I get sick maybe 1 or 2 times a year. Same goes for DD.
^I imagine your DD places her hands on the toilet seat to steady herself. Toilets spray germs into the air and on everything around them- fecal germs. (You can look this up, if you flush with the toilet seat up the fecal germs basically blast into the air- they have videos that show how most of our toothbrushes have fecal bacteria on them from this.) :
Same for when you're just peeing. You're touching the flusher (same flusher you touched after a #2) and possibly lifting the toilet seat etc.
Cleanliness after using the toilet is important if you want to avoid things like stomach bugs, the runs (the kind you can catch), and other things we carry in our lower GI tract that can make us sick.
Basically the bathroom is "contaminated" so if you touch things you touch after taking a #2 even if you haven't taken a #2 you should wash your hands.
And I wasn't raised or told to wash my hands, I just realized when I got older and had a baby that I needed to wash after diaper changes poop OR pee so it was also vitally important for grown ups too.
That's my train of thought anyway, and the health department agrees. (My husband is a chef, and people not washing their hands after using the restroom for any reason is a major cause of food borne illness.)