Sure, a CEO doesn't need to be an engineer because the CEO doesn't do any engineering, but he understands the fundamental forces that shape the success of the engineering projects and he respects the process.
Like Steve Jobs?
> CEO with an engineering background
I mean, Lisa Su and Jensen Huang are great. But I'd argue that Elon Musk is terrible as a CEO.
I mean, you're asking the very basic Bill Gates (Programmer background) vs Steve Jobs (non-programmer) question. Obviously there's a difference, but I wouldn't necessarily say that the lack of engineering background hurt Steve Jobs.
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I'm not entirely sure if an engineering background is necessary to be a good or bad CEO. The most important thing is being able to lead your workers. For some, it means being a technical leader, understanding the code and product.
For others, like Steve Jobs, it means being a visionary and making the right business choices. Another great non-technical CEO would be Warren Buffet, a great CEO and visionary: being able to predict the future of the American economy and place investments in the right place.
There's lots of ways to lead and inspire others. We programmers worship technical leaders, because that's our strength. But I'm aware of many other styles of leadership, and respect that too (Steve Jobs, Warren Buffet)
But that's not the important part of government. The important part of government is:
1. Identifying parties who might be affected by a decision.
2. Informing / talking with said parties.
3. Deciding if said parties have conflicts of interests / biases to consider.
4. Making a decision afterwards.
Expertise in a particular subject is... kind of not needed. There are always more experts out there. The only "expertise" needed is again: the politics. Being able to identify conflicts of interest and account for them.