I think if Kagi was the established leader and Google was the challenger you would be saying the opposite.
One could also argue that google is a pretty nice word for the English language since it evokes words like "look", "oggle", "oodles", implying looking through a lot of stuff and having a playful tone. Sounds silly but when someone says words sound like they mean something, it is a real phenomenon due to the way we interpret various sounds. In most languages, B sounds sound like big and round things and K sounds sound like sharp things. There have been studies on this. You can then get more specific in the subconscious patterns people recognise when you narrow it down to a certain language. This is why I say, Google is a great word for its function in the English language.