It's true that many mythicists don't use the term or use other equivalent terms. Raphael Lataster, for example, uses the phrase "JMT proponent" ("JMT" stands for "Jesus Myth Hypothesis"). It's also true that some who did identify as mythicists have backed-off somewhat. For example, after Dunn's devastating criticism Wells wrote: "it will not do to dub me a 'mythicist'
tout court." (
source). If we shouldn't identify Wells as a mythicist completely this is because he is something of a mythicist (hence the qualifier
tout court).
Luckily, labels need not be self-applied to be accurately applied. Terrorists do not typically refer to themselves as such and nor do spies, the most modest people cannot by definition identify themselves as being very modest, and Richard Carrier has identified himself as a classical scholar in print and denied that he is one in print (and has identified himself as an historian with a doctorate in philosophy despite what his CV asserts his doctorate is). And WL Craig can call himself a historian all he wants, but this doesn't make the travesties he tries to pass off as historical research any more historical research than it makes his attempts at physics actually scientific.
RM Price wrote "Virtually everyone who espoused the Christ-Myth theory has laid great emphasis on one question:
Why no mention of a miracle-working Jesus in the secular sources?" Of course, he immediately follows this with "Let me leapfrog the tiresome debate over whether the
Testimonium Flavianum is authentic" (which Crossan responded to by saying that "Price's comment...is not an acceptable scholarly comment"). He thereby "leapfrog
" over a central piece of the very evidence he claims those like him ("Christ-Myth" theorists) hold. More importantly, he identifies himself as a mythicist when he writes (in the same contributing paper) that evidence like "varying dates...are the residue of various attempts to anchor an originally mythic or legendary Jesus in more or less recent history". This is mythicism.
Likewise, when Acharya/Murdoch wrote "the gospel story of Jesus is not a factual portrayal of a historical master who walked the earth 2,000 years ago but a myth built upon other myths and godmen, who in turn were personifications of the ubiquitous solar mythos and ritual found in countless cultures around the world thousands of years before the Christian era" in her book The Christ Conspiracy, she could have followed this with "I'm a devout Christian". She'd still be a mythicist.
When Gandy and Freke write two books lying about the evidence for their view that, not only did Jesus not exist, but that the "original" Christians suffered a hostile take-over from the "literalists" (their word for those who believe Jesus was an historical person) they are mythicists. When Doherty writes the same book twice and concludes each time that the there was no historical Jesus, he's a mythicist.
Questioning the historicity of Jesus is called "history", "historical inquiry", "historical study", etc. One cannot write historical Jesus research without questioning his historicity. From works as credulous and uncritical as those by Craig, Bock, Bauckham, etc. to the moronically pseudo-critical skepticism professed by those like Carrier and Crossan.
The so-called quest for the historical basically started, in the 1700s, as an attempt to undermine the entirety of Christianity:
"the argument over the existence of Jesus goes back to the beginning of the critical study of the New Testament. At the end of the eighteenth century, some disciples of the radical English Deist Lord Bolingbroke began to spread the idea that Jesus had never existed. Voltaire, no friend of traditional Christianity, sharply rejected such conclusions, commenting that those who deny the existence of Jesus show themselves "more ingenious than learned." Nevertheless, in the 1790s a few of the more radical French Enlightenment thinkers wrote that Christianity and its Christ were myths."
van Voorst, R. E. (2000). Jesus Outside the New Testament (Studying the Historical Jesus). W.B. Eerdmans.
Although in the late 18th and early 19th centuries Christianity still had more than a bit of a grip on universities, the critical attacks on the foundations of Christian belief was made in the context of an intellectual climate which forced them to play their opponents' game. So rather than appeal to theology, faith, etc., they actually pretty much invented much of modern historical-critical study and IE/comparative/historical linguistics:
"The first application of critical cognitive values in conjunction with new theories and methods to generate knew knowledge of the past from present evidence was in biblical criticism...Theories and methods that were developed in biblical criticism were exported next to the analysis of ancient Greek and Latin texts" Tucker, A. (2004). Our Knowledge of the Past. Cambridge University Press.
"Where does lexical semantics find its materials?...One source of examples is philological research into older texts, specifically, classical and biblical philology. Because the interpretation of the Greek, Latin, and Hebrew texts is often not immediately obvious, classical scholars naturally came across many intriguing instances of polysemy and semantic change." Geeraerts, D. (2010). Theories of Lexical Semantics. Oxford University Press.
The mythicist arguments regurgitated online and in popular works were asked and answered in the 19th century (and even parodied). Even radical critics like Bultmann (frequently quote-mined in online and other popular sources) were tired of those like Drews and Frazer who kept recycling the same "hypotheses" and questions while ignoring how they were already answered (actually, that's unfair- Frazer spent years editing his voluminous work in order to try to both defend his thesis while not making a fool of himself after the plethora of scathing criticisms he received for blatant errors). Modern mythicists regurgitate the same bunk asked and answered by the 60,000 19th century biographies of Jesus the great historian Michael Grant castigated for failing to sufficiently deal with the real questions concerning Jesus' historicity. Grant was also highly critical of most 20th century works before his 1977 Jesus: An Historian's Review of the Gospels. However, he still wrote "we can no more reject Jesus' existence than we can reject the existence of a mass of pagan personages whose reality as historical figures is never questioned."
Like mythicists, from the early 18th century through Grant, those who have directly addressed the "Christ-myth theory" have rarely used the term "mythicist". Yes, the term didn't exist during the period in which these arguments were new or fairly new, and yes we have seen increasingly less works directed towards mythicist arguments as these have gone from recycled to tired to flogging possible fossil evidence of a dead equine. This includes scholars like Bultmann commonly cited by mythicists despite their disdain for the position.
"A rose by any other name" would be just as wrong. Bauer, Carrier, Doherty, Drew, Freke, Gandy, Loman, Murdoch, Pierson, Price, Robertson, etc., did and can continue to borrow something from one another and those like (albeit that "those like them" became more and more hacks and online quacks and less and less those even capable of reading the primary and secondary literature let alone being members of academic circles). They have continued to espouse similar views with slight variations. Above all, they have continued to promote the view that our evidence supports the idea that Jesus didn't exist.
That, not what they call themselves, is what makes them mythicists.