It is because they are not transliterated directly, but "latinised". Their standard English form comes to the language through references and translations in Latin, where the K sound is represented by the letter C. These latinised forms became standard long ago (often before the original Greek texts were available even to scholars) and are now accepted as English words, and as the standard English way to refer to Ancient Greek names. This applies even in cases where the dual purpose of the post-classical Latin C as both S and K has changed the pronunciation of the name.

Among scholars of ancient history, there are some (myself included) who like to opt for a more direct, "hellenised" transliteration. I spell my username "Iphikrates" with a K, not the common latinised English "Iphicrates" under which you'll find my namesake in encyclopedias. I find that it looks a little more authentic, and as you say, it often conveys the pronunciation more accurately. It's a matter of personal preference.

That said, like most scholars who do this, I am inconsistent. Some latinised forms have become so ingrained in the discourse on Ancient Greece that more faithful transliterations look outlandish and strange. This would actually impede communication. I already run into this problem here on r/AskHistorians: whenever I write an answer about Sokrates, someone will ask why I'm spelling it that way instead of the "Socrates" they've seen everywhere else. If I started referring to ancient authors as Thoukydides, Platôn and Ploutarkhos, people would not be able to chase up my references, check my sources, or find further reading for themselves. So I compromise, and say Iphikrates and Alkibiades but also Macedon and Corinth.