> Better to be a little inconvenienced and take longer to get home
How much longer? In my jurisdiction the cops can hold you for 24 hours (or something like that) without formally charging you.[1] I do not believe that this is very different to other places.
TBH, the only reason they don't usually do it to the wrong guy is because cops like to have a decent set of evidence before detaining someone. If they waste their time on someone who probably isn't going to get convicted, then they aren't looking for the person who probably will get convicted, and their comparative statistics looks bad.
So, yeah, there's a fine line.
Piss off the cop for no good reason and you'll get home ... eventually.
Be polite but say as little as possible and you'll not waste more than 5m.
Be talkative and there's a good chance you'll incriminate yourself of a crime you never committed.
[1] After which time they have to either charge you or let you go.