Personally, I'm not opposed to the providing for your children through inheritance. I do find it funny, though, that most people say you can improve your condition if you work hard, that those that have currently earned it all for themselves. That dismisses the notion of inheritance, about the benefits that brings, and about how much better off a child is when their parents are better off. An argument for a different day.
The problem with inheritance comes when you talk about ideas and culture. The content we experience, the world in which we live, shapes our culture and our lives. I learn how to sing Happy Birthday as a child, I'm going to carry tradition forward and teach my children how. Only problem is that.. oh ya, that oh so famous Happy Birthday song, so much a part of our culture, is copyrighted, and will be for quite some time (ref: http://www.snopes.com/music/songs/birthday.asp). With the rate the copyright extensions are going, 2030 is being optimistic for something of that nature to come to the public domain. That's just one example, a really obvious one, but it applies to most creative works.
The whole idea of copyright is a construct that we people made up. We wanted to give incentive for people to create works for us to enjoy, so we said 'you can have exclusive control over that work for a limited time'. That exclusive control includes the right to control when, how, and why it is copied. The one question that I have yet to have answered is this; How exactly do you provide incentive for a dead man to create more works for you to enjoy? Adding to that, what incentive is there to their children to create works if they've been given a money train they never had to work for?
If there is incentive for the children to continue their parent's legacy, it wouldn't stop just because their parent's work was in the public domain. They would have the same incentive as any other creator. They just wouldn't have a flow of money from something they didn't make. The only reason we have copyright extensions as far into the future as we do is thanks to corporations attempting to retain control of works long past. They have no care for providing into the public domain, only extracting works from it, told in new ways, that they can then copyright and profit from for a long time.