The reason so few believe it is doable is because they see so few women doing it. And the reason so few do is because they don't see it being done.
The unfettered promotion of formula in the 60s and 70s almost killed off breastfeeding in this country; there is a 'lost generation' of mothers who can't support and guide their daughters because they have no experience of bf.
There are also pervasive myths about the 'benefits' of fomula (e.g. ff babies sleep better) and a total lack of acceptance of and pathologising of normal infant feeding and sleeping patterns, so many women think that bf is 'not working' because they have been given a totally unrealistic idea of how a newborn should feed and behave, given erroneous proxies for adequate milk intake to do with baby's sleep, spacing of feeds, level of contentment when awake etc when actually the only useful proxies are weight gain (realistic weight gain, expectations are massively inflated by formula prevalence) and nappy output (again, expectations distorted by formula prevalence, but in the opposite direction, so concerning low output may not be picked up on). Women are constantly given the message that because the transfer of milk from mother to baby cannot be measured, their bodies and the natural function of those bodies cannot be trusted.
Most importantly the life of a new mother now is often totally at odds with the commitment required to establish breastfeeding in the early weeks. Bf can seem impossible when you are under pressure to snap back into a perfect shape, resume sexual activity, take 'me time', share direct babycare 'equally' with dad, resume sole care for any older children, let baby 'bond' (i.e. spend time alone with) other close family, all ASAP whether that is what the mother wants or not. It is what she is told she SHOULD want - 'your body back/your life back' is the oft quoted goal. Which is great for mothers who want that, and now have the option of formula feeding to liberate them to do so. Crap for mums who just want to hibernate with their newborn and learn the challenging but innate skill of breastfeeding together, being constantly bombarded with the message that what they want is wrong, difficult, obstructive, selfish, lazy, boring.