My uncle was a cop for 30+ years (including being Chief of Police in Vallejo, CA) and over the years I have has several good friends in law enforcement. The problem is while we know we are doing something innocent and legal, the officer at your door doesn't necessarily know that. They are taught to be suspicious (usually for their own safety), add to that they are lied to almost all the time (oh, I didn't know I was speeding, that is my friend's weed, I only had two beers!). So in the end he isn't just going to take someone's word.
Yep, there are cops out there that will give anyone a hard time just because they can, but in my experience the last thing most cops want to being doing is bugging someone. Maybe I've been luck but anytime I have been harassed by a cop it was usually because I was doing something stupid.

I will happily give up some of my time if it helps a cop do his job, which should be ensuring that we are all safe. Yes, we have the right stop them at the door... but if showing them around ensures they don't have to come back, well fine by me. Of course, if the cop demands to come in vs asking professionally (which is not always nice but professional works for me) I might tell him to stuff it (politely). But if the guy is just trying to do his job, well...