I don't buy the "it was a bad image for both companies". Do either of these companies really care about their image specifically when it comes to AD, other than simply "winning the market"?

Yes, absolutely.

I am very hesitant to use Uber because of their other ethically questionable tactics. This whole suit was furthering the notion that Uber has no limits to their desire to be number 1 - regardless of who they exploit or harm on the way.

Brand image matters a ton to both companies because they are fueled on user trust. Uber asks you to get into a car with someone you’ve never met. Google asks you to trust them with your entire digital footprint. If people have an “icky” image of them it will yield severe financial damage.

Why both companies?

The judge was admonishing Waymo for showing what were essentially marketing materials to the jury in closed-door sessions. Their lawyers were showing clips from Wall Street in court. They were asking Travis Kalanick to explain video game terminology in ludicrous detail. And so on.

No company that aims to be taken seriously wants to be involved in a circus like that.

IIRC it was in the context of Kalanick/Levandowski quoting stuff and using these terms, so it's fair to present the jury with a "here's what they meant by it and what they were referencing".

For Uber I think it's obvious. For Waymo, well, to use the Words of former program manager Chris Urmson in a late 2015 letter to Sergey Brin (Which Uber's lawyers trotted out as part of their defense) "Over the past 6 months we have stopped playing to win and are now playing to minimize downside."

Waymo joins Tesla and Baidu as self driving car companies who have levied lawsuits over top engineers leaving their projects to become competition.

How was it negative for Google?