C is actually the copier of K in this case. In the Greek alphabet, the sound you describe as "hard C" was originally represented by Kappa (K), and C itself originates more closely to gamma (Γ) which you can see how it looks like half a C, which was originally used to represent the /g/ sound.
The next step forward would be into the Etruscan alphabet, where a more C-like symbol for gamma would be used for both the /k/ and /g/ sounds.
View attachment 505041
The Roman/Latin alphabet would be derived from the Etruscan alphabet and inherited this double meaning of C. It wasn't until
Spurius Carvilius Ruga came along to invent the letter G by adding a tail onto the C to differentiate /g/ and /k/.
So to answer your thread's question, if K never existed and C always made the /k/ sound instead, then the letter G probably wouldn't look like a C with a tail because it wouldn't have been based on C, and there would probably just be another letter that would end up being used for the same purpose as the original Latin C was in the place of K and G to represent the /g/ sound, and alt-universe C (in the role of Kappa) and neo-G (in the role of gamma) might have been merged together in the Etruscan alphabet to become neo-C in the end anyway, so alt-C would be the equivalent to K and your name would be IhateletterC and you would be praising neo-C as superior to alt-C in this alternate reality. Truly, there is no end to this vicious cycle.
Sources:
https://ultrasaurus.com/2003/08/the-history-of-the-letter-c/
https://en.wikipedia.org/wiki/C