How many burglaries and realmpettynthefts went in investigated because these cops were busy with this crap?
Not as many as you'd think, I'd wager. The old sarcastic response to a speeding ticket of "I'm glad all the
real crimes have been solved if you're worried about giving me a ticket," isn't really valid. That is to say, the lack of investigation is usually independent of what the beat cops are spending their time on.
Depending on the jurisdiction, beat cops don't do much in the way of investigation except for interviews and evidence gathering for minor crimes when initially responding to a complaint. Once they pass the case on to the detectives, it becomes the job of Investigations to throw it into a stack on their desk and either ignore or pursue if there is already lots of evidence. Every so often a uniform will pursue something a little further (especially if it is time sensitive) but their real job is not to play CSI and gumshoe. If something high priority does pop up, police on other calls will drop what they are doing and respond immediately.
That said, it seems to me that there are better ways to solve this problem than arrest and criminal prosecution.
