Got to agree with you on the title :)
I am however a bit struck by your idea, because I happened to think about exactly this scenario the other day: Google being (legally?) required to provide its own competitor... I believe there have been cases like this in other industries before.
Thinking about it, you are combining two ideas here, tho: Having G set up a second engine is one thing, giving that alternate engine a totally different angle as far as historic data is concerned is something else, and depending where you'd take that latter idea, your history-fair engine would be so different from nowadays Google that it might not even be a real competition any longer.
I believe there is some wisdom in "there have two be at least two halfways balanced players in each game".
One example that comes to my mind is the way government funded TV stations are operated in Germany: The state finances TWO state owned stations, which are run by completely separate organizations, just to make sure there is a bit of choice & variety (of course there's a zillion private stations around, too, don't get that wrong). And it does work to some extend, you can notice that there are slightly different flavors to the two stations reporting, and a bit of competition to serve the better formats.
Now, to try to get back to your thread-title, and following your thought, G would not only need to provide a second engine, but it would also have to make sure that the traffic now leading to google search would be evenly divided between itself and its new "competitor". That is pretty much insolvable, because people would expect to reach the same engine any time they "google", so a random redirect won't work, right?
So, only viable option would be to include another "little league"-tab right on google (nice naming suggestion!) for what you and me would consider good websites with valuable information, an idea that has been suggested in different forms by quite a lot of people.
But adding such a tab is not competition, it's a new nerdish feature that only a fraction of users will ever use.
Side note: We'd need a separate thread here on the forum to rant about SEO for the "littleLeague"-Serps, then too, and guess what... they'd be spammed and tricked as much as anything that has been offered in the past 30 years.
The longer I think about it, even if people at G realized there was need to do something for the sake of humankind, it would be quite hard to come up with a viable solution.
Since anyone non-G seems to be stuck in the box of thinking "there is no way one could ever come up with a really competing and equally free-to-use search", its a bit strange to expect google itself to make it happen for us - they know best it would be less profitable.
Brainstorm mode on:
As long as their market share is above 80%, they could (also be forced to) hand over lots of technology and/or crawled raw data to the public, and say: "Now you've got what we can give, and you can build your cool search thingy and present the finest results that suit your taste - but you'll have to find your way on how to fund that yourself, and you'll have to convince joe public your product is worth a second visit!" - that would be fair, and hard enough to tackle.
If G offered (was forced to offer) a prominent link to some random competing search engine on top of its serp ("view alternative results for "your search" on xxx here") to help promote the idea (may be for as long as its market share is above 85%), then that might be a way to really change things, if then the competing engines really do a good job.
That could be done, and it would help G prove they are not some greedy monster but care about variety... they could probably continue to surf the 84-86% market share area for decades, too, because most people are quite happy with their product.