The original question (paraphrased) was:
How do architects manage accidental complexity in software projects?
Accidental complexity arises when those with direction over a project choose to append technologies that are one off, and that the overall strategy of the project's original architects did not intend to bring into the project. For this reason it is important to record the reasoning behind the choice in strategy.
Accidental complexity can be staved off by leadership that sticks to their original strategy until such time as a deliberate departure from that strategy becomes apparently necessary.
Avoiding Unnecessary Complexity
Based on the body of the question, I would rephrase it like this:
How do architects manage complexity in software projects?
This rephrasing is more apropos to the body of the question, where the Feynman algorithm was then brought in, providing context that proposes that for the best architects, when faced with a problem, have a gestalt from which they then skilfully construct a solution, and that the rest of us can not hope to learn this. Having a gestalt of understanding depends on the intelligence of the subject, and their willingness to learn the features of the architectural options that could be within their scope.
The process of planning for the project would use the learning of the organization to make a list of the requirements of the project, and then attempt to construct a list of all possible options, and then reconcile the options with the requirements. The expert's gestalt allows him to do this quickly, and perhaps with little evident work, making it appear to come easily to him.
I submit to you that it comes to him because of his preparation. To have the expert's gestalt requires familiarity with all of your options, and the foresight to provide a straightforward solution that allows for the foreseen future needs that it is determined the project should provide for, as well as the flexibility to adapt to the changing needs of the project. Feynman's preparation was that he had a deep understanding of various approaches in both theoretical and applied mathematics and physics. He was innately curious, and bright enough to make sense of the things he discovered about the natural world around him.
The expert technology architect will have a similar curiosity, drawing on a deep understanding of fundamentals as well as a broad exposure to a great diversity of technologies. He (or she) will have the wisdom to draw upon the strategies that have been successful across domains (such as Principles of Unix Programming) and those that apply to specific domains (such as design patterns and style guides). He may not be intimately knowledgeable of every resource, but he will know where to find the resource.
Building the Solution
This level of knowledge, understanding, and wisdom, can be drawn from experience and education, but requires intelligence and mental activity to put together a gestalt strategic solution that works together in a way that avoids accidental and unnecessary complexity. It requires the expert to put these fundamentals together; these were the knowledge workers that Drucker foresaw when first coined the term.
Back to the specific final questions:
Specific methods to tame accidental complexity can be found in the following sorts of sources.
Following the Principles of Unix Programming will have you creating simple modular programs that work well and are robust with common interfaces. Following Design Patterns will help you construct complex algorithms that are no more complex than necessary. Following Style Guides will ensure your code is readable, maintainable, and optimal for the language in which your code is written. Experts will have internalized many of the principles found in these resources, and will be able to put them together in a cohesive seamless fashion.