People who haven't gotten into habit of googling stuff in the last 20 years might not get into it at all anymore because of how search engines are gamed with SEO spam tactics nowadays
The horrible reality is that Bing has actually become a competitor to Google, simply by Google getting worse and worse. Microsoft used to be the main bad guy, but these days they practically seem benign compared to the others. Not open source like you're saying, of course.
The infrastructure to crawl, store, and serve search results to billions of users is phenomenally expensive. A government might fund it (which comes with its own concerns), but a non-profit will struggle to compete.
There's actually a lot of theory and early work out there on the topic of federated search. While existing search aggregators like Searx and YaCY certainly qualify as federated, search infrastructure built from the ground up with decentralization in mind would look very different.
Wikipedia probably has the resources to do it, wikisearch. Somebody talk them into it. But yeah, modern search engines, pretty amazing the ones from two decades ago actually worked better.
This could be interesting. The infrastructure required to scrape the internet though is going to be so daunting. Google got to build it up slowly as the internet got bigger. Bing is backed by a huge corporation that already has data centers. A new non profit player is going to take a huge coordinated effort.