It's not that the model is better than the cheaper plans, but experimenting with and revising prompts takes dozens of iterations for me, and I'm often multiple dollars in when I realize I need to restart with a better plan.
It also takes time and experimentation to get a good feel for context management, which costs money.
But, let me suggest that you stop thinking about planning and design as "prompts". I work with it to figure out what I want to do and have it write a spec.md. Then I work with it to figure out the implementation strategy and have it write implementation.md. Then I tell it I am going to give those docs to a new instance and ask it to write all the context it will need with instructions about the files and have it write handoff.md.
By giving up on the paradigm of prompts, I turned my focus to the application and that has been very productive for me.
Good luck.
You're not telling me to do anything different.