If a mother is EBF there is still plenty that the father can do. My husband did nighttime nappy changes, took the baby every morning for a 2 hour stretch in between feeds before work, and did all the housework and cooking for us all when my babies was tiny and breastfeeding was a round the clock commitment.
I've known some dads sulk because their partner is EBF and the dad thinks he can't "bond" with the baby as he can't give it a bottle. A friend of mine had this situation and her delightful mother in law was the one making this argument (ie it's selfish of my friend to breastfeed because then dad/granny don't get a chance to bond). Obviously changing, settling, bathing, walking baby around in the pram or sling, or supporting the mum and baby together by making sure the house is sorted out aren't good enough opportunities to bond. Funny that.
I've spent the last 4.5 years pregnant and/or breastfeeding, so obviously it did and does work for me and my babies. Not necessarily for the reasons I expected when I was first pregnant, though. For me, breastfeeding seems to have settled my hormones in a way they weren't before - I have PCOS and never had a regular cycle until my periods came back after DC1, and then I found getting pregnant with DC2 very easy. I also found it much more convenient than bottle feeding, after those first few months.
Every family is different though and if it's a choice between breastfeeding + depressed, resentful mum and formula + happy, well rested, loving mum then obviously formula wins.