No title of nobility shall be granted by the United States: and no person holding any office of profit or trust under them, shall, without the consent of the Congress, accept of any present, emolument, office, or title, of any kind whatever, from any king, prince, or foreign state.
From Wiki: "The Title of Nobility Clause is a provision in Article I, Section 9, Clause 8 of the United States Constitution, that prohibits the federal government from granting titles of nobility, and restricts members of the government from receiving gifts, emoluments, offices or titles from foreign states without the consent of the United States Congress. Also known as the Emoluments Clause, it was designed to shield the republican character of the United States against so-called "corrupting foreign influences". This shield is reinforced by the corresponding prohibition on state titles of nobility in Article I, Section 10, and more generally by the Republican Guarantee Clause in Article IV, Section 4."
In the US nobility = inherited wealth. Currently we can inherit $5.5 million dollars ($10.9 million combined from a married couple) tax free, and any amount over that is taxed at 40%. Needless to say, very few people actually ever pay inheritance taxes because few have those kinds of assets and those who do know how to shield their money in Trusts and the like.
Here is one place we could use real tax reform. Let's limit the amount that can be left to $1 million per beneficiary, anything else should be taxed at 100%. This won't solve the wealth gap, but it would be a good start.
There are plenty of ways to help your children succeed on their own without leaving them lots of money. If you are rich you can send them to the best schools and provide them with many other benefits. Accidents of birth still create plenty of advantages and disadvantages, but at least we can limit the creation of a noble class with such reforms.
Plus, if the super rich are unable to pass on their multi-millions, they will be more inclined to spread their wealth around to benefit more people before they die.