When I went to the classes offered by these teachers, I found that they had systematic, principle based, body centered explanations for what they were doing. Not only could they do amazing technique, they could teach others to do so.
I place this point as a key omission in aikido instruction as I observe it today. I do not believe many aikido instructors have a systematic curriculum which is based on [any] foundation. We have a lot of "soft" instruction in aikido which allows students:
A. To replicate mechanical movement without critical feedback
B. To implement technique without focus or intent
C. To develop a repertoire of unrelated techniques to apply in a variety of situations
The good news is we don't offend anyone because everyone is doing, "their own aikido," and students keep paying rent. The bad news is we reap what we sow; we are talking about a generation of aikido students who neither possess the internal skills to expand their understanding of aikido technique, nor will their physical aikido hold up in contest with other martial artists. (And yes, I understand that not everyone wants to "test" themselves, but just because I don't drop an apple on my head it doesn't mean I can ignore the effects of gravity - good aikido is good aikido and will hold its own under test).
We have a challenge to produce solid, functional, intellectual aikido students. Arguably the current system is not accomplishing these goals en masse, perhaps it is on an individual basis.
I appreciate those instructors like Ledyard Sensei who seek to develop that curriculum and substantiate its development with foundation. Case in point: I recently attended a semiar with Ikeda Sensei and it was hands-down the best seminar I have seen him give (and I have attended many of his seminars). The key difference? Sensei's delivery explaining his movement and how that movement alters the relationship between uke and nage prior to executing technique.