On Jurisprudence and the New Deal

A question I've had on mind lately that I would love a response to:

Why is it that most New Deal-era jurisprudence (1937 and later) was ever regarded as Constitutionally sound precedent. Moreover, why is it that this jurisprudence, particularly regarding the powers of the federal government, continues to be viewed as binding precedent?

The basis for my question is that this jurisprudence primarily resulted as a direct or indirect result of Roosevelt's various court-packing schemes. Wasn't this an interference with the independence of the federal judiciary that should be a cause for considerable skepticism of any post-1937 decision pertaining to the powers of the federal government?

I know that there is a certain general need for certainty in the law-hence the generalized respect for precedent. However, these decisions (and their progeny) in my mind create uncertainty by almost completely ignoring or rewriting the text of the Constitution. Is the problem just one of being unable to put the toothpaste back in the tube? Or do judges now view this decisions as having a perfectly legitimate basis despite FDR's illegitimate influence on them? Or is the problem really just one of lack of courage on the part of the judiciary branch, Con Law professors, and members of the SCOTUS Bar?