When Wicca began, everyone was a Traditionalist: they were members of covens that trained them in the ways of the coven and put them through an initiation ceremony. How then does one justify describing non-initiates and eclectics as Wiccans?
First, it is very common for Traditional covens to describe all members as Wiccans, including the Outer Circle members i.e. those not yet fully instructed and initiated.
Second, the use of the word Wicca to denote a follower of Gerald Gardner’s religion does not date back to Gardner. In all of Gardner’s writings, followers are called witches and the religion itself is called witchcraft or the witch-cult. The word Wicca was applied later, probably by Alex Sanders. As the eclectic population started to boom, many Traditionalists staunchly insisted that these newcomers should only be called Wiccans while only properly initiated followers were the true witches.
So, regardless whether or not we call the uninitiated Wiccans, we clearly can’t make everyone happy.
Third, vocabulary is formed through common usage of the word. People who invent nonstandard uses of a term are likely to gain confused stares as they refer to felines as dogs or softballs as cheeseheads, for example. Whether the Traditionalists like it or not, Wicca has been commonly used in reference to both Traditionalists and Eclectics for several decades. The toothpaste is out of the tube, so to speak.
Fourth, it isn’t just Eclectics who believe they have a right to the term Wicca. There are many Traditionally trained and initiated Wiccans today who also freely apply the word to Eclectics.
Fifth, Gardner’s religion is in and of itself highly eclectic. He borrowed from Celtic holidays, witch folklore, Greek mystery religion, the magic of the Golden Dawn, reincarnation beliefs from the East, and the liturgies of Aleister Crowley, just as examples. It seems to me a wee bit arbitrary to suddenly say “the eclecticism must immediately stop after Gardner.”
Sixth, Gardner appeared to have expected his religion to be an evolving one. Books of Shadows were not supposed to remain stagnant but were to change over time according to needs and understanding. It’s arguably one of the reasons personal BoSs are supposed to be destroyed on the death of their owners.
Finally, there is a difference between an initiation and an initiation ceremony. The ceremony is what a coven puts you through when they judge you ready. They need to judge whether you are ready, however, because the unprepared are highly unlikely to experience the actual initiation, which is exposure and understanding of the mysteries. Initiation ceremonies are meant to evoke initiation, but they are not one and the same. You can experience the mysteries outside of a ceremony.
I can certainly accept that the experience of mystery should be a central goal of all Wiccans and that reaching that experience is probably much easier with the formal training and tested rituals of a coven. But Eclectics can certainly still pursue and experience it, and I see no reason why they should need a separate word to describe themselves simply because they’re doing it on their own.