About 5% of the ships transiting Great Belt do not use pilots. And unfortunately, it is the wrong 5%! It is most often old tankers with less than perfect equipment who don't want to pay for pilotage on their way to or from Russian or Baltic ports!
I know the director of "dan-pilot" (he was an instructor with the maritime college I attended) and they are less than impressed by these ships as they often bring themselves as well as other ships in danger trying to navigate a notoriously difficult stretch of water (as you probably know, route T isn't exactly the widest route out there)!
The reason why we still don't have compulsory pilotage is because, especially, the russians start complaining each time it is brought up! If they were intending on taking pilot, they probably wouldn't complain about it being compulsory!
If you plan on calling a danish port, however, and you haven't taken pilot, through