Nobody's saying you have to benefit other people's children. You can work for
your own benefit. As soon as you start providing for your children, you start breaking the fundamental premise of a pre-scarcity society; they now get to live off of something they didn't work for. (This isn't merely a capitalist principle - everyone from St. Paul to the Jamestown colonists to Vladimir Lenin said, "He who does not work, neither shall he eat.")
That said, if you just care about wealth inequality, it's totally fine to buy your child a modest house, or even buy them an expensive house at a large marginal tax rate. As the paper points out, you don't need to stop all intergenerational wealth transfers, you only need to stop a portion of the wealth transfers of the richest people at the far end of the RNG.
The trick about "a house," in particular, is it means two things - a place to live and an investment vehicle. I agree that many people will be sympathetic to the argument that you should be able to provide your kids with a place to live. (I am myself somewhat sympathetic to it.) But as long as there are people on the streets with not even a bed, it's immoral to twist this sympathy into a right to transfer millions of dollars in wealth to your kids in the form of an expensive house on expensive land. So, put a cap on the inheritable amount that makes it quite sufficient for reasonable living quarters, and heavily tax transfers beyond that.