This isn't true; they have no relation to one another. It definitely wasn't a "well, since we are taxing the estate, we should create a step-up basis".
The step-up basis was the result of Treasury Decision T.D. 2690 in 1918. The modern estate tax went into effect in 1916.
The step-up basis is likely simply a mistake influenced by UK norms. The tax code was created from whole cloth by regulators that had never done it before. (Congress basically passed the buck, abdicating responsibility to Treasury to figure it all out.)
Treasury made several errors of basic logic in the early years, some of which were subsequently fixed, others (like step-up basis) weren't.
On the UK influence: back in 1913 the UK (and most other countries at the time) didn't tax capital gains at all. The law passed by Congress implied that capital gains should be taxed but the drafter of the law (it was written by a single person) was surprisingly confused and vague on the subject giving five or six different possible interpretations of what he meant.
And so: step-up basis. The original 1913 income tax law didn't say what should happen. Over the next several years Treasury grappled with the issue, and related capital gains questions, effectively a "first time in history" kind of solving the problem.
From a history of early errors in the tax code by the Treasury:
"Beyond mere error, there was the influence of the income tax of the United Kingdom––the foreign income tax most prominent in the minds of the drafters of the 1914 regulations––which did not tax capital gains at all. As Marjorie Kornhauser recounts in her work on the early history of capital gains taxation under the federal income tax, from 1913 until 1921 Treasury’s interpretation of the income tax as encompassing capital gains was controversial, and it was unclear whether Treasury’s interpretation would withstand judicial challenge. If total exemption of capital gains was thinkable because of the UK model, then basis rules allowing for widespread self-help exemption might have seemed unexceptionable. In addition, the trust law distinction between principal and income––under which capital gains are assigned to principal rather than income—may have influenced Treasury’s misunderstanding of the role of basis in an income tax. Finally, there was the statutory declaration that income did not include the value of property received by way of gift or bequest. For regulators not accustomed to the distinction between deferral and exclusion provisions, it would have been easy to overread the statute as implying a permanent exclusion rather than as merely being silent on the question of permanent exclusion versus deferral."
The Treasury decision was enshrined into law in 1921 -- based on the Congressional testimony of a single person whose testimony has been described as "not his finest hour" due to logical errors like this that went unremarked upon by the Senators -- cementing the mistake permanently due to a failure to apply consistent logic to taxation issues.
The claim that one should get a step-up basis because of the estate tax is obviously nonsensical. If you sell the assets before death, you pay both the capital gains tax and then the estate tax. But if you don't sell the assets before death, you only pay one tax.
There is no logical explanation for why the application of both taxes should occur if the sale happens before death but only one tax should apply if the death happens before the sale.
In 1976 Congress got rid of the step-up basis in the Tax Reform Act of 1976.
Due to intense lobbying by rich people, it was restored in 1980.