In the USA there’s due process required for authorities to gain access to your private data

This is only the case when the data is being obtained by traditional means. As we've seen recently, authorities buying data from data brokers completely circumvents any sense of due process on a technicality.

Yeah, always invoke your right to remain silent. [...] It baffles me how criminals will sit there and let police interrogate them until they confess. Maybe it’s because they think they can talk their way out of it, but then why confess.

Oh absolutely. Even if you are entirely innocent, the police use psycological manipulation as routine part of interrogation. They'd sometimes rather you get confused as to whether you actually may have done something wrong, and eventually admit to something you didn't do, than to let you go as innocent. There is absolutely nothing good that can come out of "cooperating" (such a loaded and innacurate word in this context), whether you're innocent or guilty.