So if you fail to object in a timely manner, and the evidence comes in, that's different from objecting and having the judge erroneously let it in. We want habeas to provide an incentive to get things right at trial: to internalize the enforcement of constitutional rights. "Prejudice" means that you have to show the error wasn't harmless. "Cause" means that mere mistake is not enough-- there has to be a reason. A 6A violation can be a "cause."
So Fay and Wainright represent liberal and conservative views of what habeas is for, and how it should be used. We saw much more expansive usage of the writ when constitutional rights were expanding. Some of this was a function of who was on the court, and some was a function of just general historical developments.
Of course, that gets you over the procedural default, but it doesn't address the merits.
By the way, Wainright didn't define what cause was, other than to say that a mere mistake doesn't count.
Linkletter v. Walker decided that the exclusionary rule announced in Mapp v. Ohio didn't apply retroactively (i.e., when you have a substantial break with precedent, people previously convicted can't use that precedent on collateral review). See p. 945: look at the purpose of the rule, the reliance of the states on prior law, and the effects on the administration of justice of applying the rule retroactively. See, e.g., the discussion of Stone v. Powell on p. 953 footnote: 4A exclusionary errors can't be raised on habeas, because the purpose of the rule is to be a deterrent to police, and it's too late for that.
So the bottom line is that habeas is about the legality of detention-- it's not a stand-in for SCOTUS on appeal. It just checks to see whether the law was properly followed.
Now the court has to balance between the articulation of new rights and the need not to treat similarly situated litigants differently: the first guy to make an argument that justifies a right would get relief, but not those who asked that right to apply to them later. And we also don't want to issue advisory opinions. So we decline to offer retroactivity on habeas, and we won't announce new on habeas unless they would apply to everyone.
So, the two exceptions to the rule against retroactivity: