A serial number on a $3,000 piece of computer equipment is rather different than a serial number on a $5 bill.
Some people do know the serial numbers of all their $5 bills: http://www.wheresgeorge.com/
True. Nevertheless, I still don't know the serial November of even my laptops, let alone my cell phones.
And I sure as heck have never noted the serial # of any banknote I have owned. It doesn't spend enough time with me for me to bother noting down the serial number of bank notes I use.
If I drop a banknote on the street while taking something from my pocket(and I have), I know I'll never see the money again(and I don't), and whoever finds it, is probably going to keep it.