A publicly owned search engine, that will absolutely not be used for propaganda purposes by, say, the Department of State, or by a megalomaniac elected representative.

Need to build consent for a war with <Country>? Give me access to the search index, and a few weeks, and it'll be done.

A government owned search engine is 100% bad idea, it will cost a ton, it will cost more than equivalent business developed one, it will be abused by governments and law enforcement, your traffic will be combined with government data to make a last century dictatorship police state weep for joy be a money maker for people you very much don’t admire

most of all there is no public value for it when the government can legislate operators