The other thing that is wrong with this sentiment is that "privacy" is not a binary thing: you don't "have privacy" or "not have privacy". You don't "want it" or "not want it".
Privacy and the need for it, is heavily dependent on context. You want more privacy when watching porn than when watching some sports. You want more privacy when you are a minority than when you are part of the ruling class. And so on.
Edit: so a person wanting to escape religion and seeking online help on how to do so needs different privacy than three friends having an online beer. Everyone has moments and time where they need (some) privacy. So probably 99% (a made up statistic) has a need to replace software in some (rare) context, over privacy matters.