I'm going to come right out and try to express the source of my unease regarding b/f a much older child- let's say beyond toddlerhood.
Nutritionally it is not necessary in the first world. I clearly see the case for extended feeding in places where the diet is somewhat inadequate, but a fine balancing act has to come into play between the mother's nutrition needs balanced against her need to be available to all her children, not just the feeding one.
From an antibody point of view, the point is maybe more relevant, with the difference that by 5, say, the child has probably been exposed to most of the same pathogens as its mother anyway, especially in less developed countries. So a moot point whether it is still useful as a disease prevention measure.
Emotionally, a child begins to grow beyond its immediate surroundings and take an active interest in the world at around 5-6 years of age. They come across upsetting things, both at school and at home as they try to push their boundaries. It is my perception that continually bringing the child back to its mother as a source of comfort prevents it from developing coping strategies of its own. Furthermore, and this may be purely Freudian, a bright child should be moving beyond the oral gratification phase by 5-6, so need neither mummy nor dummy as a comfort object by then. The dummy in gob thing at 7 shocking imo. (which does not even begin to cover my attitude to dummies per se, but hey...)
A fair proportion of the extended b/f children I've met had some kind of speech defect. IMO this as something to do with still using their tongues and mouths in a relatively infantile way. I do not see this as an advantage in any way, in fact quite the opposite.
As a parent, I see it as my job to help my children grow to independence. We live in a society where our children can and are independent intellectually at a fairly young age. They have a lot to learn, arguably far more than other apes, and have as humans to be very flexible intellectually. I do not see staying stuck in the infant stage as far as comfort goes as assisting that.
fwiw, I b/f mine for 14 months (stopped due to pregnancy and unbearably sore nips); he was not ready to stop on any level, but it was OK.
Second one b/f for 17 months. I selfishly wanted my body back after 3.5 years of continual pregnancy and b/f. She was not quite ready to stop. My third was a violent feeder (punching, poking, grabbing and twisting (wince)) and I longed to stop from about 12 months. We kept going anyway, to 24 months, and weaning was very easy and quick.