I feel like I should clarify. Just because I'm the default doesn't mean that dh doesn't ever care for them. Especially once they wean, my dh takes a big role in their care. He's just gone during the week (he doesn't work an enormous amount--maybe 50-55 hours), and little kids aren't awake for all that long that isn't "work hours", especially during the week.
When my dh is home, he is totally in the dad role. On Saturdays, he gets everyone up, dressed, breakfast, and often, he takes my older two boys (they are 2 and 4) off somewhere or outside gardening. He cares for them without me. It's still usually up to me to plan something for lunch--either out or at home--but if I'm not home, he'd take care of that.
In the evenings, dh plays with the boys (all 3) between supper and bedtime. He gets home right at suppertime, or he'd play/care for them prior to that, too. He helps with bedtime for the older two (he can't really nurse the baby--LOL).
At church on Sundays, our two younger boys sit with us. Dh is completely in charge of the 2 year old (again...I get the baby, cause it's not like he can nurse him). Two or three nights a month, I leave in the evenings to do whatever. I go to a worship service at church, cooking classes, sometimes I grocery shop alone or go shopping for something that is hard with the boys (bras, anyone?). Dh is completely in charge then, and he does fine.
So, for us, default doesn't mean mama does it all. It just means that caregiver is my main role, as provider is his main role.
Just re-read the OP.... I guess my dh sort of "asks permission" if he's going off/planning something out of the ordinary. I'm not jealous of his shower/getting ready alone, cause it happens at 5 am! And, I am appreciative that I don't have to get up that early. LOL. In our house, things are usually phrased like, "Oh, I need to go to Lowe's. Is that okay with you?" And, I can ask him to take a kid or (if I need to get away), I can offer to go instead of him, or I can suggest the whole family go. So, I guess while, technically, he has the freedom to just up and go somewhere, he doesn't really. I can't remember how this came about, so I don't have any good advice there. Same thing happens at night--he'll say, "hey, I want to do something Monday night. Will that work for you?" So, I have a chance to give any input I need to (hey, I'm overwhelmed, can I have a night, too? Can you make it later or earlier? Stuff like that). And, on Saturday mornings, he always takes care of the kids so I can sleep late.
But, in my house, yeah, having a baby changed just being able to pick up and go for a walk without announcing it to everyone and figure out what all the other people in the house were going to do while I was walking (are they staying home? going with me? Is dh busy? Can he keep an eye on them?). It was just part of the whole seismic shift of parenthood for us. For both of us, really.