There are probably multiple reasons, but decades ago, a buddy of mine had a dad that worked for Phillip Morris, and he took us on a tour, where the tobacco was squeezed till all juices were removed from the cigarette tobaccos used in cigarettes, leaving just a cellulose close to sawdust, and then the juices were mixed with all sorts of stuff and added back into the tobacco cellulose, making a new tobacco product that is injected into the cigarette tubes. Thus, they knew the percentages of nicotine, because they had added that much nicotine, along with all sorts of flavors.
Pipe tobacco is a much more natural product, where all sorts of things determine the amount of nicotine that occur naturally, so blends can vary year to year, tobacco to tobacco. It would require testing of every crop used in a blend, and it would be very expensive.
That said, percentages of nicotine in a blend would be moot or unreliable. Virginias actually have a lot of nicotine, but the acidity affects the way the nicotine can be absorbed. So, when we hear that burley has much more nicotine than Virginias, what is really meant is that we can more easily absorb more of the nicotine from burley. Testing it would probably not give us an understanding of how we would actually feel the nicotine.
As a side note, when I visited LaPoche and heard Mark Ryan talk about perique, he mentioned that perique doesn't actually have a lot of nicotine, because the fermentation process reduces the nicotine into more complex molecules. So, smoking straight perique doesn't actually give you a huge nic hit. But, when mixed with other tobaccos, the acidity and more complex molecules make it easier for the pipe smoker to absorb more of the huge amounts of nicotine already present in Virginias that would just pass by without being used by the smoker.
That said, there are probably whole lists of reasons that would go along with these.