I think if Kagi was the established leader and Google was the challenger you would be saying the opposite.

No it's the actual word. "google it" allows for a liaison between the two words because "google" technically ends with an l sound (a consanant) and "it" begins with with a vowel - "googlit". It's also a soft sorta rolling consanant, which helps. In the case of "kagi it", "kagi" ends in an I and "it" begins in an I. That means you have to make a hard stop between the two words and pronounce clearly to differentiate between one I and the other otherwise you lose the words entirely. The two words fail to flow into each other in any way, making them feel less like a pair. Phrases that are easy and satisfying to say in the sense that they are actually just easy to get your mouth around are more likely to catch on. This is definitely something they should consider more carefully.

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.

What happened to simply using the verb “search”? Or phrases like “look it up”? It shouldn’t really matter (typical conversation) which search engine a person is using.

I say ‘cellotape’ for any old tape, I say ‘cellophane’ for whatever is in the drawer. I say ‘biro’ for pens and say ‘twink’ for that white stuff.

I don’t think it really matters as long as meaning is there.

Though ‘Google’ is starting to mean ‘ad infested trash’, so maybe the word will lose favour.

Kagit

Cage it. As in enclosing the answer, and capturing the essence of it.