I believe that you need to have a concrete understanding of what the forms are meant to be used for, what is accomplished by training them, and how to go about that. This also means that you need to know what forms are NOT meant to be.
In my opinion, forms are often viewed as performance art. They are the vehicle used to show off or highlight the techniques contained in a system as a way of entertaining an audience. Or they are viewed as the end product of the training: "see, I know kung fu, watch me do this form." Or they are simply added on as a curriculum requirement, often just before a test, to give the student something to be tested on, and often quickly forgotten afterward.
In my opinion, none of the above are what forms were meant to be, although I understand how they have evolved into these things in the modern era.
Forms are a tool that you use in your training. They are not performance art. They were never meant to be put on display for the uneducated public to gawk at. Nobody was meant to see your forms other than your teacher who teaches them to you, your classmates with whom you train, and your students to whom you teach them. To anyone else watching them, they are one tool taken out of context and become meaningless as abstract movement. It would be like looking at a screwdriver all by itself and trying to understand how it is used to build a house. Asking to see someone's forms is somewhat like wanting to buy a house and asking to see the builder's toolbox. The house is the product, the tools in the toolbox were used to build the house. The forms are a tool within the greater toolbox, and they are used to build martial skill which is the end product. The form itself is not the end product. You work with them and use them to help you develop your skill. They are never "done." You have never mastered the form, and in fact the concept makes no sense because the form is not to be mastered, but rather to be constantly worked on as a vehicle to greater skill, not as a end in-and-of itself.
I believe that not all forms/kata etc. were created equal. Some were poorly designed and no amount of training or delving into "deeper" secrets will turn them into valuable training tools. I have learned some forms that I classify in that way. Over the years, as my understanding of my training has improved and I have gained higher quality instruction, I have rejected those forms once I was able to identify them as such. In other cases, the form itself may have been well designed and has a lot of good training to offer, but it may have been poorly taught, so everyone in the downstream is not learning it well. If you don't understand the form and you don't have an instructor who can give you quality guidance on it, it has little value, even if it is a famous form for which everyone sings its praises. Practicing it is a waste of time and offers nothing that cannot be gained better, through other types of training.
@skribs I know from other discussions that you have struggled with finding value in the forms that you have learned. I am in no position to judge the value of TKD forms because I have never learned nor studied them, but from the input of other members in those discussions, it is not a foregone conclusion that they were simply poorly designed and inherently hold little training value. However, they may have little value to you. It may be that they were poorly taught to you so you struggle to see their value. It sounds to me like they were often taught as "curriculum fillers" just before a test, expected to be forgotten quickly. You were the rare student who did not forget them, but that does not negate the fact that they were probably poorly taught to you so you view them as shallow curriculum filler, or as performance art done to win a trophy in a tournament and to dazzle an uneducated audience. Given your plans to open a school, I don't know if the forms would hold much value in your school. I don't have an answer to this problem, I am simply pointing out the fact that the problem exists and somehow you need to make some decisions about that.
Getting back to your original question. I use the forms as a tool for training, not as an end product or as curriculum filler or as performance art. I am in no hurry to teach them, because there is a whole lot of fundamental material that is used to build the student's foundational skills before the form itself can be learned and have value. And I make no secret of the fact that the foundational skills are far more important than the forms. If one were to study and train the foundational material only, and learn to apply it well, that person could become a highly skilled martial artist without ever learning a single form. The forms simply take the foundational skills to a higher difficulty level which raises the level of training, and opens one's eyes to a wider horizon of what is possible. The forms are learned gradually, and we make it a part of our regular training moving forward. It isn't the only thing we work on, and we spend more time on other things than we do on forms, but it is a regular part of what we do. Over and over. Sharpen the knife on the stone.
Given that we don't do belts, there is no concern over making sure someone knows this or that form in time for their next test. It is a non-issue. Our forms are very long and rather complex, and cannot be learned in a weekend. They take weeks and months to learn, and then years of practice to polish the skills that they build. It is an ongoing process that is never finished. And there is a certain order in which they are meant to be taught, but I believe that order is not carved into stone as absolute. And neither does one need to learn them all, for them to have value. They are not a "complete set" in that way. Some people might have a need for more forms, other people for fewer. If the lessons the forms are meant to teach are grasped after learning five forms, then learning another five may be meaningless and unnecessary. On the other hand, if one has not grasped those lessons after learning five forms, then I am not sure learning another five will be helpful, and the extra material might simply spread your training too thin and make it more difficult to develop your skill. Forms teach concepts and options, but do not define the body of curriculum. So you don't need to learn all the forms in order to have a legitimate claim on the system. In my opinion, if you have learned the forms, they are valuable tools, but at the same time, if you have not learned the forms, you are not necessarily missing anything. I know that is a bit of a paradox, but it is the conclusion at which I have arrived.
When the teacher decides a student is ready to learn the next form, then that process is begun. But it does not hinge on "mastery" of the previous form, because that term has no meaning in this context. But they should have a solid grasp of the first form before the next one is begun. And the process continues to open one's eyes to a wider horizon of possibilities.