All comments here focus on extreme cases: The police viewing you as a possible suspect, FBI becoming interested in you etc. Here is a much more mundane problem: Using Tor (even a VPN) while logging in to most big Silicon Valley firma that make money with your data (LinkedIn, Facebook, Tinder etc.) will result in your profile being suspended REAL FAST with the only way out to upload your gov't ID, i.e. complete deanon…
Unfortunately, no solutions in sight.