For me, I just bring a package of crackers, some water, then go out in the streets with my kids, visiting nearby playgrounds or lots with trees. They'll then start playing, perhaps needing a little help getting started, and my involvement is mostly coming up with a plan for where to go next, and watching out for signs of exhaustion. So most of the time, I'm actually not active.
I also enjoy having limited help with say cooking or cleaning, but yeah, that's exhausting, because you need to multitask and both do the job and monitor their state and the job they are doing.
In countries where men have mandatory paternity leaves that are significant this imbalance is greatly reduced.
You could actually spend time on thinking what you could do with your kids.
Why did you get kids in the first place?
But even if what you say is true I'd still say he doesn't want to be a parent. You don't pick and choose with parenthood.
There are people who have the opposite experience and people who feel ok with both.
This idea that parents should uniquely and equally be caretaker for their kids is absolutely against biological reality for a lot of people; I'm happy to be around my kids for a limited amount of time (and the less they're toddlers the more I can spend with them without going insane) but my main contribution is providing them food, shelter and protection.
My mandated paternity leaves, while being economically advantageous, were an absolute nightmare.