I think that there is something to remember: to be productive with the help of a tool, you need to learn how to use the tool first. You know how to walk, and you can get from point A to B in an hour. If you want to get there faster, you need to learn how to drive, and those days that taught how to ride could be used for walking. But as soon as you know how to move, you are much more effective.
It is like frameworks - the car is the foundation.
With wireframes in general, they are used to facilitate and speed up the development process. To apply the DRY principle, you will get reliable basic tools (word processing, input control, form validation, email and session processing, etc.) so that you can immediately work on them so that you do not invent the wheel. I was happy to use the framework, but as soon as I received it, this is something that I can not let go, in my experience.
I don’t think this is a limitation (since they are extensible), I think it’s rather a “personal standard” - the way these applications should have been written in the same way as when creating your own libraries. Once you know and love your framework, this wave will magically disappear.
About MVC, I would not use the word "should", but this is a definitively good choice, no matter what you do - if you use the framework, great, and if not, but you separate the business logic from the content, great! It's all about you, feeling comfortable. The same thing happens with Grid Frameworks, CSS Resets, using libraries, etc. is a matter of choice. What is mine Use these tools because they are designed to use and create trusted applications and websites. They were tested again and again, they work, and they help you not to repeat yourself and not to reinvent the wheel (which has been done a thousand times). MVC is also great for scalability and maintenance.
My recommendation is exploring the framework. There's the reason you chose Cake over Codeigniter (I don’t know why, though - the Codeigniter user is here!), So stick with it and work with it for a while. They are all powerful, but the full potential is not fully visible from the very beginning.
In addition, the last: since all applications have punctual use, you will always create your own libraries, no matter what, and these frameworks simplify the creation, use and support. That way, you can have a mix of all of them, with the whole database of the framework.
Keep trying - you won’t regret it!
My two cents.