There are often implications that simple-minded people are not as smart or can be perceived as not understanding all the details. On the contrary, I believe that some of the smartest people and best leaders I know have an amazing ability to simplify complex things. Here are a few examples of situations where keeping it simple is an advantage.
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Message

How do you describe your company and what they do? I meet with a lot of entrepreneurs that even after reading their pitch deck or hearing them talk for a couple of minutes, it is still unclear. Think about what is the four-word message that summarizes the essence of what you do. This is valuable internally for aligning your team and making clear the focus of what you do. It is also valuable externally to potential customers and investors that shows you know how to break through the clutter.

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Analysis

There is a tendency to overanalyze decisions. This could be around pricing, markets to go after, process improvements, etc. While it is easy to boil the ocean and run lots of numbers, I find it more valuable to have a clear hypothesis on what you are testing to guide the analysis. Then think through what is the summary decision based on the data. Having a clear executive summary that is simple and actionable shows your ability to really focus on what matters in decision making. Having simple pricing makes it easier for the customer to understand and not be confused about what they are paying.

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Value proposition

I meet with a lot of entrepreneurs that love talking about all the cool product features in their tech. But it is more helpful to focus on the simple value proposition of why your potential customer will get value from your solution. Potential customers are far more likely to buy something that helps them double their sales leads versus something that has a laundry list of cool features and reports.

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Remember there is tremendous power in taking something complex, and simplifying down the message, analysis, or value proposition to something that others can grasp.