Because by that definition Firefox has been adware since Firefox 1.5, released in 2005, due to the ubiquitous "Google" logo in the search box that every user sees by default upon installing the browser, and for which Firefox receives the bulk of its revenue.
That's significantly more defensible (it has to search somewhere by default, and most engines are known by their logos, and Google is the only search engine worth a crap) than imposing paid sites on you by default.
Search has been a basic part of using the web for years now. All browsers support the OpenSearch standard. Now, you may feel it would be better for a user to have to manually add Google to their search bar, but relegating search entirely to an extension is an odd suggestion.
