I breastfed all my kids to at least 18 months, and was fairly involved in some groups for mums nursing toddlers, and while I think there is a lot to recommend it, one of the things we saw in the group time and time again was mums afraid to set boundaries on their toddlers around breastfeeding.
And of course these kids did use that leverage to try and control their mothers, they are smart about that kind of thing. If they know mum will always stop what she is doing and sit with them, you can be sure they will take advantage whenever they want some attention. Which is a lot of the time.
I remember one mum in particular who was having issues with her little boy biting her on purpose, probably to get a reaction. I suggested that she just put him down, say they were done each time, and go do something else for at least 20 minutes. (In my experience this works very quickly to extinguish the behaviour, often within a day.) This mum said straight out that she thought if she did this she would traumatize the baby, and that when a baby wants something, it needs it. She was really scared she'd screw him up for life.
I do think this kind of attitude is more common among mums doing extended breastfeeding. But it's ignorant about how toddlers are different from babies, in a lot of ways, and it doesn't do the mums or kids any favours.