Though it is uncomfortable for some in our culture to acknowledge, breastfeeding for 2-7 years is the physiological norm. Anthropological studies bear this out. I find it interesting that extended breastfeeding has to somehow be proven to beneficial or justified. It's the norm, it's what our species has done for millennia - so rather than talking about "benefits" of extended breastfeeding, why aren't we framing the risks that we (as a society) take by feeding infants and children in a new, different way than our species ever has before. Probably on an individual level this isn't that much of a big deal but on a population level, it is.
I think if we had the kind of society and culture that enabled and/or encouraged all mothers to breastfeed well into early childhood, we would see less SIDS, SUDC, obesity, cardiovascular disease, cancer, tooth decay, allergy/atopy, respiratory and gastrointestinal disease on a population level (some of these applying to mothers as well as infants/children). But this assertion will be very difficult to prove conclusively, because it is not possible to design an ethical double blinded trial of extended breastfeeding Vs the non-physiological and extremely modern alternatives. Unfortunately there is no financial incentive to investigate this other than from a public health perspective - there is not and never will be money to be made from making breastfeeding easier to do.
It's also very difficult to separate the loss of extended breastfeeding from other massive shifts in our culture, diet and lifestyle.
But how could switching away from the physiological norm (with lots of evidence that breastfeeding positively effects affecting airways, gut, immune system, nervous system, metabolic system etc) in ways that we quite literally don't understand ever be something that we assume to be good? This is purely cultural. You won't find a reason for to stop "extended" (itself a misnomer) breastfeeding on somebody else's terms other than vague subjective judgements such as it makes them uncomfortable, surely it's time to stop, what is the reason to do it, etc etc. This thread is a case in point, it boils down to "this is normal for human beings and has many benefits" on one side and "I just don't like it" on the other.