Presumably the reason to use Google search is because of the following reasons:
A) Google does the heavy lifting of indexing and presenting the site in a searchable format.
B) Google offers the greatest flexibility when it comes to search types and queries.
C) It's free
D) Implementing a powerful search solution on Steemit which is a blockchain based platform, might technically be difficult and hard to scale.
I guess the duckduckgo search engine could be used, if we want google to dissapear we should have our websites prepared for it