He switched on the air, and a pleasing coolth pervaded the room.
I can write that he switched on the heat and a pleasing warmth pervaded the room, right?
So what’s wrong with coolth? Why would we treat it as uncouth?
Don’t bother saying it’s a non-word made up on analogy with warmth. They both come from the same formation, the one that also gave us truth from true, depth from deep, strength from strong (with a vowel alteration), length from long (ditto), sloth from slow, and a few others. And coolth has been in the language since the 1500s at least. It just happens that it has fallen out of favour in recent times and is now used mainly for humour or cuteness. You can still find it in the dictionary.
What are the alternatives? There is coolness. That, like coolth, adds a suffix. It looks perhaps more normal to us now; new words are still being made with ness. But it’s a longer word, and it lacks the minty fresh final sound of coolth. And would we brook warmness? Our alternative is just cool: “In the cool of the evening,” for instance. That uses an adjective as a substantive – in other words, it’s a conversion of an adjective to a noun. We do it with cold: “Come in from the cold.” But we don’t usually do it with warm or hot: “In the warm of the room”? “I have come to appreciate her hot” (rather than hotness)?
And what would the harm be of keeping forms parallel, and having a distinct and concise and soft cold word for the condition of being cool? Why must it now be just a funny form, a word-that-doesn’t-exist-but-should? I really can’t tell you why it has fallen out of fashion and become uncool.
But what we certainly see is that English does not hew much to logic and elegance and all that. No, it goes by what is cool and couth, what we are habituated to and what we have learned. Here is a rule; here are exceptions. Here is a word you see all the time; here is a word you would expect to see quite often but it just doesn’t show up. You infer that the words that should be there but aren’t are somehow, for some reason, uncool. Lacking in coolth, and therefore received without warmth – except the warmth of mirth. Words that match patterns but aren’t used are taken as signs of poor language understanding (we learn early that small children and illiterates use words like goed). And so, though they are cut from the same cloth, they are considered uncouth.