Sorry to join so late, but have taken ages to read the thread!
Wow, this is an interesting one! I am battling with my feelings on this...
I am breastfeeding my 11 month old DD and hope that I can continue to do so until she self weans. If I am totally honest, I don't think that I would allow her to continue to feed when she starts school. I am ashamed to admit that I am too influenced by what other people think...this must be the reason as I can think of no other reason why we would stop as I fully believe that children should be allowed to self wean.
With regards to breasts being sexual...I think that if we teach our children about the primary function of breasts from an early age then there should be no issue. To a breastfed baby or child, breasts are a source of nutrition and comfort, they are not sexual. If my DD asks me when she is 7 what breasts are for I will be telling her they are for feeding babies.
IMO, the whole sexual argument just highlights what is wrong with society - at 7 years old children should not even be thinking about the sexual nature of breasts, or about sex or sexual relationships at all. We are allowing our children to be prematurely sexualised in so many ways and this worry that a 7 year old may see breasts as sexual is awful! Maybe I'll be called naive for having this view 
IMO there is no point in discussing if we would feed our babies aged 15 - studies have shown (I think!) that the natural weaning age for human infants usually falls between the age of 2.5 and 7 years old, therefore, it is a pointless discussion, sorry.
And with regards to need - well infants who continue to breastfeed as toddlers may not depend on breastmilk if they are eating a healthy balanced diet, but the breastmilk that they do consume is still nutritionally significant, and still has so many benefits.