If you know me IRL, you know that my (male) partner is our household's primary cook and launderer. We share parenting more equally, but we have each been the primary parent at various times. I have a few thoughts about this.
One of my BFFs asked me one time, when she was a new mom, how it was that my kid was so close to their dad? Her baby only wanted her, and her husband was quick to hand the crying baby off to mom and admit defeat.
My answer: You've got. To leave. Them alone together.
Nobody can develop a close, trusting relationship if that relationship is always being observed and mediated by a third party.
We had the same barriers to this as every family. I was the breastfeeding parent, and I was home more in the first couple years.
But leaving the kid alone with their dad meant that they developed their own way of dealing with each other. He didn't comfort the baby the same way I did. He had a different sleep routine (with some similarities, of course.)
This was good for all three of us!
But what if I was constantly there, so the baby knew that the comfort of breastfeeding was just on the other side of that door? It would have been harder for the two of them to work things out without me.