Why would it be up to Google to decide whether or not DuckDuckGo gets to "be around"?

I am also confused about this wording but I assume it refers to the duckduckgo-app on android devices. It would be blatantly anti-competitive if google would refuse the ddg app in their app store, solely because they compete with them in the search-engine market -- there are legal mechanisms against this behavior.

Agreed. And there are laws against this sort of thing, and the regulators are slowly but surely catching up to the fact that they will have to start actually enforcing them.

It's not always a bad thing. The duck.com domain used to redirect to Google for a long time (they got it in a random acquisition) but now it's been changed to DDG instead. I'm pretty sure that this kind of analysis played a role there. (A more diversified ecosystem in search also helps with fighting SEO spam, which is by far the biggest actual threat to Google Search volume.)