I'm confused by the notion that "double taxation" is something this is obviously to be avoided.

Let's say that a billionaire sells $1 billon of appreciated stock a year before their death, and pays the full capital gains tax on it. They die, and their heirs inherit the $1 billion of cash. Would you argue that it would be unfair for these heirs to have to pay an additional inheritance tax on this because this would be "double taxation"?

Presumably not, or if you did, presumably it would be because you believe that inheritance tax is inherently bad, and not because the tax was already payed. Alternatively, consider the same scenario where the was no capital gains, and instead the stock was sold at the same value it was purchased at.

This isn't to mean your conclusion is necessarily wrong, but I think you should look closer at your argument to see if it's as strong as it should be.

I just mean that so far as the invention/calibration of the taxes, the idea was that a high estate tax would offset the reset of capital gains. I don't have a strong position on whether the laws do this well or make full sense etc.

Though I'll note that the scenario you pose never really happens. A billionaire isn't going to cash out a billion dollars of stock just to have cash to sit on. They're either doing it to spend in on consumption (nothing to inherit anyway) or to buy a different asset that would itself have capital gains assigned.