What's the relevant part of building a search engine that's affected by network effects?
Is it the index itself? There's already a fairly decent open-source equivalent to that in the form of Common Crawl, which has been out since 2011. People (including me) have tried to build search engines off of it, but it never seems to work quite as well as Google.
Is it the computing infrastructure? That's already been commoditized and offered as a service by multiple providers - AWS, Azure, GCP, SoftLayer, etc.
Is it the serving infrastructure? Commoditized by ElasticSearch, which uses many of the same techniques as Mustang and in many ways does it better.
Is it the ranking algorithm? It used to be that Google would agree with you. However, the ranking algorithm changes basically continuously - the one in use now is very different from the one that was used when I left in 2014, which was different from the one where I learned how it worked in 2011. I've heard the new one is heavily machine-learning based: given a suitable training set and some learning-to-rank papers you could construct something similar.
Is it the log & clickthrough data? Imagine the privacy advocate conniptions if that were open-sourced. AOL got in huge trouble when they open-sourced their click-logs circa 2002.
Is it the evaluation system? Mechanical Turk exists, and Google's rater guidelines are public.
I'd argue that the real competitive advantage of Google now is the brand and associated consumer habits, and it's really hard to break up a brand. Same reason Coca-Cola remains dominant 150 years after they started selling cocaine-laced sugar water. This is a recurrent problem in the economy today - brands fuel not just Google, but also other giant monopolies like Coke, Nike, J&J, P&G, DeBeers, McDonalds, Wells Fargo, and so on, and in many cases the companies that own them get to practice some exceptionally bad behavior. But short of reaching into each consumer's head and getting them to consider each purchase on purely rational factors, I don't see how to fix this.