So you've made a comparison with a dummy, but it's a poor one.
Breastfeeding facilitates a moment of closeness and connection with the mother.
Breastfeeding is discrete event. It starts and then it finishes, the child moving onto something else.
Breastfeeding for a toddler cannot be conducted at the same time as going for a walk, playing with toys, exploring, interacting with others etc
Whereas a dummy can sit in a child's mouth, indefinitely, preventing them from using speech whilst they engage in a wide variety of activities completely ignored by their parent.
And I'm not trying to demonise dummy use, I'm sure there are times that using a dummy is totally fine and a helpful comfort tool, but worst case scenario is above which can negative and is linked to poor speech development. Which I expect is why you are trying to liken breastfeeding a toddler to sticking a dummy in.
And yes actually, far from being hypothetical researchers in several countries have already measured a modest positive correlation between duration of breastfeeding and increased educational attainment and IQ. Why don't you Google it?
(Can't attach the image unfortunately but here's a link: https://www.thelancet.com/journals/langlo/article/PIIS2214-109X(15)70002-1/fulltext)
This graph is from a prospective study carried out in Brazil, published in the Lancet, for instance.
You are right that this is a topic meriting further investigation - but who will fund it?