NO. If the rich person dies the value steps up on inheritance, And nobody pays capital gains tax. (Although they do pay inheritance tax, which basically makes the most sense when thought of as a stopgap measure to plug this loophole.)
The step up in basis also avoids a logistical nightmare, as it can be extremely difficult to determine the cost basis of an asset owned by someone who is now deceased.
If we're not taking in enough from inheritances, we should change how the estate tax works, but eliminating the step up in basis generally would just result in a substantial increase in administrative overheads.
Finally, to the extent that there is a problem with gains totally escaping taxation (e.g. via trusts)-- the article doesn't use any of its massive felony private violation to make a case for that.
I regret repeating the double taxation point, I agree it's the weakest point-- plus, if we want to double tax as a matter of policy, we can do that. Step up really just avoids a logistic mess.
I think regardless of where you think taxes on inheritance should be, we're much better off with the step-up. If we're not collecting enough decrease the thresholds or up the rates (and if we're overtaxing earned wages as a result-- provide a method to exempt some of those from estate taxes, it's an easier accounting issue that not having the step up in basis).
(In general, brokers and similar institutions track basis, so I don’t think the death of the owner makes determining the basis especially difficult.)