It is not only in your workbook; take this dictionary:
Fam. [Uniquement en corrélation avec ça et p. oppos. à lui] Ceci.
C.− [Pour donner une réponse approximative] Comme ci comme
1. Ni oui ni non; pas trop
2. Tant bien que mal; à peu près
3. [En parlant de la santé] Pas trop bien
− [Pour donner une réponse vague, approximative] À peu près
Spéc. Pour répondre à une question sur sa santé (comment ça va ?)
Comme ça. À peu près, pas trop bien.
Comme ci, comme ça (cf.
couci-couça). Plutôt mal que bien.
[ Trésor de la langue française informatisé - TLFi, ci, ça, exemples omis ]
Larousse notes it is informal too; but neither mentions vieux or archaïque. Everything is possible within a set group of people, depending on age, region and such. Saying that "noboby" says something is a strong statement, most likely an exaggeration, which one should substantiate. It is not only about language, and one cannot ignore the possibility that less people feel so-so i.e. that more of them feel either very good or very bad; as well as the possibility that people maybe communicate less about how they feel, especially when they don't feel as good as they "should" be.
Generally, the concurrent use of ceci and cela, for more or less indeterminate things for instance, dates from the 15th, even before cela could contract into ça (the pronoun) in the 17th. Later, you have ci, ça or tout ci, tout ça (archaic). That sort of alternating, phonetic interplay on such two similar elements is the gist of what the construction is about. In my opinion comme çi comme ça doesn't feel dated or in disuse in the context you mention, and is certainly not otherwise, which doesn't mean it couldn't be elsewhere, or that it would be my first choice of answer to how are you. Couci-couça, possibly an alteration of the Italian loanword così così under the influence of the former construction, is also possible but feels less natural to me (I also personally pronounce [kusikusa], which doesn't sound the same to me as que si used as an expletive, or que ça expressing some form of suprise; one's mileage may vary, of course.). I might use comme ci comme ça as a fall back answer if someone doesn't understand something more colloquial I would use (pas pire, pas terrible, ça pourrait aller mieux, (juste) de même, mostly Québec French).
Dictionaries don't label it old or anything. It is familiar, it still parses fine by me ; it may or may not be the most usual answer to how are you, depending (is not for me), but is also used elsewhere with the idea of indeterminate approximation.