People who were breastfed for a normal length of time (eg to the age they can remember it) describe their breastfeeding experience as one of love, warmth and security. Why on earth wouldn't you want your child to remember that?
Sadly I never was breastfed, but I'm sure some on this forum will be able to pop in and tell us what it was like for them
All of my children remember breastfeeding. Not many of us set out to breastfeed an older child - but it happens. And it's a lovely experience, when they can tell you how much it means to them.