OP - I think the question you have to ask yourself is, on balance, what does he actually contribute to your family. Ok, so it's not housework obviously. So is the fact that he's good with the kids and the main earner enough? Only you can answer that.
My DH sounds a bit similar to yours in that he grew up with staff. You can't get people to do what they don't see unfortunately. Also in many cultures, men are brought up to believe that their responsibility is to provide financially and anything else is a bonus. It's a job to reprogram this.
To my mind, if he isn't prepared to do ANYTHING then, as per his upbringing, he will have to accept cleaners are the way forward. My DH does nothing in the house but he works mega hours. I have a cleaner in 3 times a week, but I doubt he's even aware of this. God knows what he thinks goes on tbh. Of course there's still all the day to day tidying, cooking, laundry, etc, but it definitely helps. Like your DH, mine is great with our 4 kids and has loads of energy for that.
But if you just think he's lazy and useless on all fronts then it's hard to respect that.