If you have as much time as you want and never get tired then sure, do it all. Most people seem to experience tradeoffs between these things but I'm sure some don't.
For the second thing, you could make that argument. Are you? Because I'm old, and our fathers mostly considered "good parenting" to be work as hard as possible outside the home to aspire to wealth and model hard work. And I don't know any of my generational peers that aim to emulate them in this, because it makes you a distant and uninvolved member of your family.
So if you're going to make this argument for yourself you certainly can. I've experienced first hand what "setting a good example" through labor does for your children.
I see what you're saying and I very well may have a father who fits the archetype you're describing but it's hard to generalize or stereotype because there's so many family dynamics at play when we grow up. Not denying your experience, I'm sure the "alpha male, hard worker" father figure (or parent figure) has had a net negative in some families but in my specific instance, it's brought passion and ownership into other parts of my life (marriage, kids, etc).
It's also made me realize that yes, I want to be there for my kids more than my dad did, but I also have personal goals related to work that I want to accomplish in my life, more macro-level goals. It's also made me more involved in my community because I want more ownership in what's going on around me. It's definitely a balance and you need the self-awareness and time management to finese it.
I know a lot of people whose parents set a good example by working hard and moving up, and were also very present to them. It’s pretty normal in my peer group for this to have been the case.
The fact that your tiny view of humanity doesn’t include those people doesn’t mean they don’t exist.
For the second thing, you could make that argument. Are you? Because I'm old, and our fathers mostly considered "good parenting" to be work as hard as possible outside the home to aspire to wealth and model hard work. And I don't know any of my generational peers that aim to emulate them in this, because it makes you a distant and uninvolved member of your family.
So if you're going to make this argument for yourself you certainly can. I've experienced first hand what "setting a good example" through labor does for your children.