This is interesting to read as I'm expecting my first imminently and planning to breastfeed, though not expecting to feel immense guilt if it doesn't work out.
I'm fully prepared to change my view once I experience the reality but based on the experience of those around me I have to say I disagree with the idea that pumping/switching to formula is likely to have a huge difference in equal parenting.
I've been reading a lot on the fourth trimester, the need for women's bodies to recover after childbirth, etc. My feeling is for the first six months after birth, it's not just about caring for a child, but supporting women to recover from pregnancy and childbirth. Men can't breastfeed, but they're also not physically recovering from a huge event. When women are on maternity leave, it makes sense to a certain degree they find themselves as primary carer with their partners supporting them. But this is why I feel shared parental leave is so important- to correct whatever imbalance may occur as a result of biology.
A lot of friends who've availed of it have said that despite best intentions, they had slipped into the woman being the 'boss' in terms of baby care- the one who knew what baby liked, could settle faster, etc. After a few months shared parental leave, they felt much more like equal parents, which then continued on.
There are obviously huge economic issues around that- not many people can afford to take it, but many people also argue it's impossible as the man is the higher earner. I am lucky enough to have a number of very good examples of equal parenting in my friendship group: in the majority of cases, both parents were at an equal stage in their career beforehand and went back to work full time after a year. They were also all mid-thirties when they had their first and had been used to sharing household chores etc equally. This shouldn't be the only way - and I'm sure there are many SAHMs who feel they have equal parenting arrangements- but my feeling is the socio-economic side of things has much more of an effect longterm than breastfeeding.
So it comes down to culture, and respect for roles, and the different ways women can be supported and valued. I'm the only one who can carry our child, or breastfeed our child. But we already have areas of responsibility in our relationship, so why not in parenting once they're not picked based on some sexist stereotype? I handle our money and bills, my husband does most of the cooking, I do most of the laundry, we ultimately share chores equally. If he feeds me while I feed the baby, is that so different once there are other ways he binds with her and takes responsibility and it doesn't carry on into areas outside of breastfeeding?