There are words for everything that we need a word for. If there is no word, then the concept/item/action/nuance is provided by a descriptive phrase, clause, etc.
In British English, the commonest recently accepted neologism is "Brexit"
Brexit, n. The (proposed) withdrawal of the United Kingdom from the European Union, and the political process associated with it.
2012 P. Wilding in blogactiv.eu 15 May (blog, accessed 19 July 2016) (title) Stumbling towards the Brexit: Britain, a referendum and an ever-closer reckoning.
2012 Christian Sci. Monitor (Nexis) 10 Oct. Why would the EU
consider special economic and trading privileges for Britain after its ‘Brexit’?
2014 Financial Times (Electronic ed.) 19 Aug. 16 In many cases,the US banks are as worried about the eurozone's impending banking union as they are about Brexit.
The word was needed, it had the motive, means, and opportunity for massive publicity. It fulfilled a need and, following the Greek threats to leave (Grexit) it was invented (probably by a person we will never know) and became popular.
There is a genre of written humour that delights in inventing words.
There is a book "The Meaning of Liff" by the genius Douglas Adams, author of "The Hitchhiker's Guide to the Galaxy" in which place-names in the UK are defined as words. (The first sequel is available at http://liff.hivemind.net/) If I remember correctly, the meaning of "liff" is "the teaspoon in the sink that you have missed washing when you drain the water."
There is a website, "The Dictionary of Obscure Sorrows" https://www.dictionaryofobscuresorrows.com/ by John Koenig who invented/created words to express concepts/items/actions/nuances that he felt were needed. The majority are very plausible and I have used one or two (with the explanation.) The website has now been turned into a book and it not so easy to browse the "dictionary".
Here are a few entries:
Sonder: The realization that each passerby has a life as vivid and complex as your own.
Opia: The ambiguous intensity of looking someone in the eye, which can feel simultaneously invasive and vulnerable.
Monachopsis: The subtle but persistent feeling of being out of place.
Énouement: The bitter-sweetness of having arrived in the future, seeing now things turn out, but not being able to tell your past self.
The point here is that inventing words in isolation is not difficult but there is a difficulty in introducing them into common speech - few ever make it to a standard dictionary - the attrition rate must be huge.
The Simpsons gave us "cromulent" (adj.) and "embiggen" (v. tr.) and, because of the size of the audience and the humour attached, they now appear in dictionaries.
Shakespeare gave English 1,700 new words (From the RSC Website)
The early modern English language was less than 100 years old in 1590 when Shakespeare was writing. No dictionaries had yet been written and most documents were still written in Latin. He contributed 1,700 words to the English language because he was the first author to write them down.
As well as inventing completely new words, he used existing words in inventive ways, for example he was the first person to use 'friend' as a verb, as well as 'unfriended’ (Twelfth Night) and from 'gloom' he invented the word 'gloomy' (Titus Andronicus).
There is always the possibility that a few/some/many of the words were in current colloquial use but, had not Shakespeare been popular, one wonders how many such words would have survived.
On another site, someone asked about the word "machinic". This appeared in a paper, written in English, by a German Professor and the context implied that it meant "in the manner done by the internal workings of a computer". The general opinion was that "it wasn't a word." It may or may not make it to general speech but the odds are against it.
So in response to "a word for there not being a word for it" I would say that such a word has a zero-to-low demand and will have virtually no publicity. Until such time as these change, all attempts are futile.
You might like to ask the question on "meta": "How many neologisms suggested by EL&U have made it into standard dictionaries?" ;)