We still may. Rights which are given up by the people are rarely regained That's why it frightens me when I see/read people saying, "just let them in, if you're innocent, you have nothing to worry about." Next it will be "just agree with them and sign this admission, if you aren't a criminal, you have nothing to worry about."
Let's put it this way. If my sister's baby was missing, and the police wanted to search my house for evidence, I think I would comply in order to speed up the investigation. There's a slim possibility that they might find some anomalous evidence that they could run off on a tangent with, but that would not offset the greater possibility that eliminating a potential suspect would make the job of finding the real perp easier.
So if you give a damn about the result of the investigation, you may want to cooperate with the authorities, and I do not see this as an abrogation of rights in the least.