If the rationales discussed in Mapp v. Ohio were retained would we have the good faith exception?
There are two major rationales discussed in this case. Either of them, taken as an absolute rule, would prevent the existence of the good faith exception. However, there are exceptions to most legal rules and those exceptions tend to be sensible. This is the case with the good faith exception.
The first rationale in Mapp is that searching someone's home is like compelling them to testify against themselves. This means it violates the 5th Amendment. If this rationale were taken as an absolute rule, even a search with a warrant would be illegal. Therefore, this rationale cannot possibly be categorical and the good faith exception does not violate it.
The second rationale in Mapp is that admitting evidence from illegal searches would make the 4th Amendment meaningless. The 4th Amendment is really meant as a check on lawless and indiscriminate police action. When police obtain a warrant, they are not acting in a lawless or indiscriminate way. They are doing what they are supposed to. If the warrant turns out to have been illegal, it is not their fault. Prohibiting the use of evidence they have found using this would not deter indiscriminate police action because the police have already been acting in a legal way (as far as they could know) by getting the warrant.
Therefore, the rationales used in Mapp should not be seen as contrary to the idea of the good faith exception.