I think there's a couple of fairly simple reasons contributing to Americans not having a culture of inheritance: first, that we live a long time by historical standards; and second, that we have a norm of children moving out after maturity. The first means that estates are generally released after children are well into their careers, and sometimes after they're themselves retired. The second means that all but the very wealthiest have to establish their own careers rather than living off the family dime.

This wouldn't directly affect actual inheritance, but it does take a lot of the urgency out of establishing a legacy. That lack of urgency might in turn contribute to reductions in real inheritance, given that you can sink a more or less arbitrary amount of money (by middle-class standards) into things like travel and expensive hobbies.