...the estate tax is paid by the estate, not the inheritor.

Though true, it's one of the all time best examples of a distinction without a difference.

Your buddy tries to leave you 100.
Option 1: The government gets 40 from the estate, and you get the 60 leftovers.
Option 2: You get 100 and then the government immediately takes 40 from you, leaving you 60.
They both quack in a remarkably similar manner, so we can consider both of them ducks for practical (quacktical) purposes.

The main reason the distinction is emphasized is that heirs can't complain about estate taxes...technically (and only technically) they aren't the ones paying it.
Plus, option 1 seems less painful, so it's easier to keep the laws on the books.

As an aside, I think estate taxes are a fine idea, properly constructed, as I think dynastic wealth is not something to encourage.
Offhand, I can't think of any reason the great-great-great-grandchildren of some 19th century robber baron should be among the idle rich as a result.
I can see that almost everybody likes leaving money to their kids, meaning very high inheritance/gift/estate taxes are so hard to get consensus on. It's almost a genetic imperative.
So I'd support rules to tax first-generation bequests lightly but old[er] money bequests heavily.
e.g., Your low tax inheritance threshold would be limited to what you inherit, less what those benefactors inherited, adjusted for inflation.
Low tax on bequests by the nouveaux riches, and high tax on old money bequests. And, by extension, family trusts.

Jim