There have been designed economies. They don't appear to be very desirable places to live.

I think you mean local maxima as opposed to "best possible .. designs"/global maxima

Nature also optimizes for far more variables than humans do. We min-max for a handful of KPIs at most. Nature optimizes for everything that an organism needs to survive, including in once-in-a-lifetime circumstances. It must do so since most organisms don't have dedicated support infrastructures. Cars don't need to concern themselves with reproducing, a jaguar does.

Sure, there are genuine inefficiencies like the laryngeal nerve but there also are plenty of apparently useless things that turn out to have some niche importance such as the appendix.

Intelligent designs economies are best associated with tyranny. See CCCP.

It's definitely possible. That's what large companies are for; they subsume some part of the economy into themselves, intelligently design it in ways that could never be found through an unplanned search, and are greatly rewarded if they do it well. Amazon, for example, found one of the best possible designs for both direct-to-consumer shipping and cloud systems.

But we don't usually think about it that way. Most people who advocate for a planned economy don't want that kind of planning; they think it's bad to innovate in things like how jobs are structured, bad have a single large company in charge of most of your shipping, and bad that Jeff Bezos can build such a good company that his stake in it is worth billions. Planned economy advocates that I see generally want the economy to work how they specifically would prefer, without much regard for whether other people think that's the best way.