NavList:

What is particularly interesting is that although Blackburne considers  the "New Navigation" a great improvement  he continues to promote  Sumner methods. The cynic in me says that is because he had devoted a significant proportion of his off-duty hours to calculating his tables and naturally he wanted to sell his books. Blackburne's books include many pages of testimonials from both RN and merchant navy officers. I have attached an example.

Maybe some navigators had an aversion to plotting intercepts. The advantage of the Improved Sumner Method (according to Blackburne) was that  position could be determined by calculation rather than by plotting. The calculations could be done by plane trigonometry or - perhaps more importantly - by Blackburne's tables.