OP,
Sorry to hear that you are going through this.
Those traits don't in themselves make a man to not do his share of house work and child care. However, they could (along with a whole lot of other factors like upbringing and life experiences) produce a level of entitlement.
I have no personal experience of a counter example, sadly!
But, looking around, I have seen quite a few who tick all those boxes AND do school runs and various other things..
You get the impression talking to them, that they are totally engaged with their domestic life, their partner and their children (be it school activities, extra-curricular, well-being, discipline). And talking to the mum, you get the impression on how supported she feels too!
They DO exist!
One example: Both professionals, mum works part-time (doctor) 1-2 days a week, dad in a leadership role, has his own hobbies which he actively pursues, but dad still is totally hands on, comes to pick up after play dates, does school run most days, is there for all birthday parties, organises work at home etc etc..
I don't know the details of their day to day family life of course.
its not really who-does-what, but the attitude towards all those things that need to be done for a household to run and for children to thrive in a happy and safe environment..
Its almost like how one defines success and fulfilment in their lives!
If they think doing their share of house work and child care is a favour then, its not going anywhere! That entitlement is what breaks it, in my opinion.
They DO exist ! But, need to differentiate between the ones who truly believe in those values and the ones who pretend to or will perhaps preach those values, but not practice them quite.
The other thing I find is also the assertiveness of the woman which seems to play a big role in how these things emerge. So, may be that has a role to play as well.