(1) Google also puts ads and other little tracking widgets (google analytics, G+ social buttons, etc.) all over the web, gathering massive amounts of information about people’s browsing habits unrelated to any direct customer relationship or informed consent.
(2) Use of Google search does not at all imply that a customer wants all of their searches to be associated with their identity, processed, stored indefinitely, used to build a comprehensive dossier to better target advertising on unrelated pages, or handed over to nation-state spooks who come asking. It’s not at all clear that most customers understand what information they’re handing over or what can be done with it when they use services like search.
[Yes, plenty of other ad networks, analytics companies, social media services, etc. do the same thing, and plenty of other types of companies (e.g. the banks you mention) and government agencies also build permanent profiles of people based on whatever scraps of data they can; this is not only a Google problem. It’s creepy when anyone does it, which is why there should be better regulatory oversight ensuring that customers know what data is collected and how it is used, restricting certain types of data aggregation and customer profiling, and placing limits on how long various types of data can be kept.]