By 2 my toddlers would be far too busy to stop for breastfeeding.They eat what we do,drink cows milk from a cup,and rarely see a day's illness,so I'm sure they're doing fine.
In a third world country,if a child's diet is good I can see the need,but I believe a healthy diet gives my toddler what she needs at 2 years old.I wouldn't breastfeed or offer formula at that age.
I think breastfeeding can easily become a comfort thing,both for child and mother,and there's a point when it's a habit rather than a source of nutrition