Speaking as a not-so-technical (never run a server) reader myself, what people like me want is not whether or not the data is on our own devices (that's an implementation detail) but the real issue of real reliability, privacy, and basically not having all the centralized bullshit that makes me feel helpless.
None of the big systems run by the big corporations are actually reliable long-term. They change stuff all the time, come and go, change terms, and generally mistreat everyone. So we just learn to be mostly passive and kinda just play the game. It's a weird and totally undemocratic form of extreme bureaucracy, and we have no idea how to do anything more than superficial.
So yeah, people don't want to take responsibility for all the data, but they do want the people responsible to actually be trustworthy, reliable, and serve the public interest. Is that just a complete fantasy, totally unrealistic?