Temanor It's simple, yes. Memorable, not sure I agree. But both of these points are semi-irrelevant.
The goal of product branding is to create a distinctive identity that helps a product stand out in the marketplace. As stated by many, "g" invokes thoughts of Google, which is weird given the product, i.e., it's distinctive of a competing product. The dog is distinct. The K, even if it was ugly, would be distinct. The key is distinct. I doesn't have to be cool or attractive, it just needs to make people think "Kagi."
If I walked by a billboard and saw a stylized "g" and next to a search bar, I'd think Google. Their billion dollar branding machine works. If I saw a "K" I might think Kagi, and I definitely wouldn't think Google. If I saw the dog I'd immediately think Kagi.
Pretty much anything that avoids being associated with google, the dominant force in search, would be better. K sounds like Kagi. The dog looks like Kagi. Those are obvious options, but anything distinct could work. Anything other than a "g" or "G" would be smart.
Look at the t-shirts being sold in the store. They feature the dog. Distinct. On top of that they have nice style, which is great, but second to distinct.
Distinct distinct distinct. "g" is distinct in the realm of search. It is distinctly Google.