That is not the "only" reason that Mozilla is struggling. There are vanishingly few companies their size who manage to remotely hold their own against Google for over a decade, let alone in a market segment that Google has invested on the order of billions of dollars in engineer time and advertising cost (some of it in the form of "free" advertising on the google.com homepage). That Mozilla has to contend with Google also being basically the only one willing to purchase search deals with them just makes it even more difficult.