All knowledge cannot be contained inside one person’s mind, one method’s pedagogy, or one era’s zeitgeist. Most singers will naturally acquire technical ideas from different sources. However, one can skim the surface of many methods, consciously or unconsciously only “finding” ideas that fit into what they already think they know. That would be confirmation bias: “In psychology and cognitive science, confirmation bias (or confirmatory bias) is a tendency to search for or interpret information in a way that confirms one’s preconceptions, leading to statistical errors.” (sciencedaily.com).
In order not to fall into a habit of confirmation bias, you should study a method that interests you in some depth. Try it for a period of time, and attempt to understand its reasons for being and take a course in it if it seems interesting. After diving in deep for a bit with an open mind, you are in a much better position to determine what you can use. If you learn some new things, that is a good sign. If you come out of the course saying “It confirmed what I already do as a teacher.” then you probably have not dived deep enough. (I have heard that quoted phrase far too often, and rarely believe it.)
Now, those “new things” may not necessarily be good things, but if you understand them within the context of the overall method in question, you can move on. Don’t reject an idea simply because it’s different. Try it first, then decide. That’s what “open mind” means.
When you find things that work for you, keep them. If you do this in a method-agnostic manner, and find yourself using technical points from several methods or teachers with different approaches, then you can truly call yourself an eclectic teacher.
There is nothing inherently wrong with being a purist either. If you favor one method after comparing it to others, you certainly have the right to that approach as your main way. However, there are many (MANY!) people who go through teacher certification programs who stop being open to anything else. Although it’s tiring to keep your mind open, it’s required if we want to keep learning and serving the singer population the best way we can.