Open source is famous for fostering a bunch of different approaches to the same problem, and slightly different forks of the same concept. That's the "bazaar" in the famous metaphor, as opposed to the "cathedral" of monolithic, hierarchical, linear proprietary development within a closed-source company.
"Everyone working on the same thing" only works well when there is broad agreement on what that thing should be, and strong governance to resolve disputes. National highway systems, militaries, and power grids are good examples.
I don't think search engines are a good example of where this would work; it's not clear in advance what will make a given search engine better. Thus we benefit from a variety of competing approaches, essentially to expand the space in which we're searching for the optimum.
Also, the broken window thing asserts that small amounts of criminal activity lead to larger amounts of criminal activity via signaling that being bad or neglectful is OK, which is both not proven and irrelevant to software writers being prone to reinvent the wheel for whatever reasons they have.
I think you would be right about the greater good being served by everyone being aligned on the same search engine ONLY IF we understood search engines so well that we knew there to be only one mathematically optimal way to build search engines.
Since we don't understand search engines that well, there is a LOT of value in the exploration over the space of search engines that these different companies represent.
The broken window fallacy argument is that those speaking of the benefits of the broken window are mistaking maintenance cost for generated value. That doesn't seem to be the case here. This is society implicitly investing in exploration over exploitation.
However they would still be able to borrow good bits from each other and gain insight on how things could be done differently, so arguably the end result would be a win. From a technical standpoint that is -I think where it gets messy is when we try to factor in the business implications.