Translated, as literally as I can, the phrase becomes something like "How concernedly/sadly/fearfully etc." Domaĝi is one of those words with no direct translation into a specific set of English words. it also has meanings like "leave no stone unturned," "to not boggle," "Wish to keep intact," "Fear for," and so on. But it does not mean damage. With the -e ending it means (approximately) Bedaŭrinde. This is a difficult word to fully comprehend.
If the sentence had been Estas domaĝe (ke, pri) the generally accepted translation would be "It is a pity (or I am sorry) that/about." We are also allowed by Zamenhof to use "Kia domaĝo."
it is also said in Esperanto: "Post domaĝo venas saĝo."
Words in all languages generally have a fixed meaning. Their use in many contexts in which another language has many words is confusing; and careful examination typically shows a complex, abstract concept can fit many diverse situations with the same meaning, even if it appears completely different.
Languages evolve complexities such as metaphor or homonyms (including words spelled and spoken the same but not related). At the same time, abstract terms convey a set of feelings and emotions which, for the most part, we ignore in favor of an implicit understanding. These abstractions are lost when given a list of translations; they become understood when communicating for a long time in a language, thanks to context and plain empathy.
Many of the things you say have a connotation of recognized damage. The last thing you said is, in an abstract sense, "After [some unfortunate thing] comes wisdom", which is a crude description of the human facility of hindsight, foresight, and learning: those things which we find upsetting, unsettling, unfortunate, or otherwise derogatory to our ideal lead us to reflect on how to prevent such tragedy. The same sense of loss and misfortune is what your mind renders as damage and destruction, and is the imperative in the effort to preserve a thing from such damage. A large number of things can be viewed and discussed as related or as a form of this abstract ideal.
Abstracts are impossible to explain sufficiently. They are only "difficult to fully comprehend" because they reflect a sense that repeats in situations, but which we haven't created large and complex descriptive words for because we took the optimal route of creating A WORD that connects to that meaning. Look at the stupid crap you get when someone tries to explain "family"--people can only explain the condition which gives rise to what they sense as "family", but they can't explain what family is at all.
I think "kia" has a similar function for nouns, like "kiel" has for adjectives and adverbs. It kind of makes sense when you think of "kia" as meaning something like "what kind of"; "what kind of a pity" works if you use "pity" as a noun, but "domaĝe" is not a noun. Difficult to translate example though... probably clearer with another word:
Kiel alta! = How high!
Kia alteco! = What (kind of) altitude!
It shouldn't be.
Words ending in -a (whether adjectives or correlatives) describe nouns. Adverbs can be used as expletives by themselves, or they modify verbs or words ending in -a. So, in your example, "domaĝe" is actually describing "kia", but "kia" is lacking a noun.
If you absolutely want to use "kia" you'd need to say: "Kia domaĝo!"