I don't think it's that simple. It's not as simple as DDG makes it out to be.
As a society, what do we want to see for the default search choice box on your smartphone ?
DDG's proposal is:
> Alternative search engines with the most market share in each market are shown on the first screen, randomly ordered. The remaining alternative search engines are available by scrolling, also randomly ordered.
Do we want to cram that with hundreds of random sites that want to be ? That amounts to a meaningless choice (nobody has really time to look through them all and compare). If people are willing to suffer that much through, they can certainly customize after the initial setup to pick whatever they want. So I think beyond the first screen is probably not a good idea - just put a search box or something.
Then, do we just put top N ? What would that N be ? Do we let the screen size dictate the number ? Do we use some fixed N ?
If you picked some fixed N, what the order should be ? From purely immediate utilitarian perspective, you'd want it to be according to the market share - to minimize the effort for people to pick what they want (with the assumption that the market share reflects the user's choice). DDG supports "random" order on the first screen - random would put them as the top choice more often than their current market share. This is not an unreasonable choice if you want to take advantage of "nudge" (of putting as the first choice) to "even out" the market share. As far as nudges go, this isn't THAT obstructive when looking from the lens of a single user, but this would still be a very direct intervention on people's choice and what companies can do - it's roughly equivalent to mandating grocery stores to pick top 5 soft drinks and display them in a random order on the top shelf. Generally we're bad at writing laws and regulations at this level of detail, so we try to rely on market to sort this kind of things out. But this question arises due to monopoly concerns in the first place, which is exactly about market distortion, so maybe this kind of intervention is OK ?
DDG also implies other search engines can bid more because they have higher profit margin due to sacrificing privacy. But this ignores two important aspects: 1) people are willing to trade off privacy for more "return" in the form of more features and free services (companies with higher profit tend to develop more, better stuff than companies with less profit) 2) companies who can't auction higher might be fundamentally less efficient than competitors, thus has higher cost structure. In that case, as a society we do generally want to use more efficient one.
So, at least part of DDG's request is not unreasonable, and does merit some discussion, but it's not as straightforward, and the answer likely will depend on how comfortable you are with how deep and detailed intervention you're willing to have the government / regulatory body decide.