I understand that with the Chaotic Soul theme only titles of posts show up in the category archive pages, but if there is no way to insert excerpts here, what is the use of the excerpt for the Chaotic Soul theme? Does it serve any purpose? Thanks.
No it doesn’t. The Excerpt works in only 21 themes. But the post editor screen is generic: you don’t get different modules for different themes.
And please paste the exact URL of your blog when asking questions here, or link your nickname to your blog (as explained in the Sticky 8 Things to Know Before Posting). We usually need that to give a relevant answer.