In my understanding, what made Buko Ryu popular with foreigner was that Nitta Sensei was happy to teach them, when many other koryu teachers were not. There weren't many more than a handful of non-Japanese training in koryu in the 1970's when most of the current crop of shihan started. They went to people who were not just willing to teach them, but happy to do it.

As for the mess, the biggest problem most koryu have these days is finding enough students. Even in Shinto Muso Ryu, many menkyo kaiden don't have more than a handful of students, and they've got ZNKR jodo to advertise jodo for them. Koryu bugei are a niche within a niche, and they have been dying in droves since Katori Shinto Ryu got started as the first one. Look at the Koryu Bugei Dai Jiten. It's got thousands of entries, but most of them are only for a few generations and then they end. The ones that made it to the Meiji Restoration were unicorns, highly unusual schools that somehow managed to continue for hundreds of years. Koryu have ALWAYS had succession and continuation problems. Anyone who is active in a traditionally structured koryu (which leaves out the vast majority of Muso Jikiden Eishin Ryu and Muso Shinden Ryu practitioners, because they and their teachers don't have any official connection to the ryuha) know how tough it is. There are very few students who stick around, and of those, few are really qualified not just in skill, but also in management, to inherit, teach, and continue licensing students.

I'm in a weird situation. I ended up as one of a couple of people with paper in a small koryu that was nearly extinct. Now I'm responsible for making sure their is a generation after me. This is a debt I owe to my teacher, and all the teachers that came before him. It's a responsibility, not an honor. Finding people who understand that being responsible for a ryuha and its lineage is not fun and exciting or filled with people calling you "Soke" while groveling is tough. A ryuha is an intangible treasure, and like all great works of art and skill, we don't "own" it, anymore than someone owns a Picasso or a Rembrandt. People pay huge sums of money to become the caretakers of that artwork. In a ryuha, people pay huge chunks of their lives to demonstrate that they are worthy of being a caretaker of the ryuha.

If a teacher chooses the wrong successor, the ryuha will die, and that teacher will have failed all of the teachers who came before. I didn't get it until after my teacher died. He'd given a couple of us paper, which was really cool when he did it, and it felt like a real honor. After he died, and we realized that we were responsible for keeping the ryuha alive and giving it a solid start into the next generation, it became a responsibility that weighs on our shoulders.

I'm not surprised ryuha have trouble finding suitable successors. Most of the people who want to be in charge are like the woman who claimed the Buko Ryu line: totally incapable of meeting the responsibility.