What is stylistic authenticity? For example, I could argue Newton's style is authentic, as is that of any other - authentic for his or her times.
Likewise, the style of those who write on the Grex or on Schola, is also authentic - it is authentic 21st century neo-Latin.
Just as we read Jane Austen and Dickens, no-one proposes that we write in pure imitation of them. Influenced, perhaps, but each writer develops his or her own style, eventually. A fluent neo-Latinist would also develop their own style, should they ever reach such a degree of fluency in the tongue that they write in it often.
The entire goal of learning to speak Latin, and write in Latin, is to relate to Latin in a more holistic way. Classical texts are not by any means the only texts in Latin worth reading. There are a great many renaissance and later texts that are worth perusing - but a degree of fluency is needed to simply be able to dip into a variety of Latin tomes, from a variety of time periods, simply for the pleasure of it.
The whole goal of the enterprise is to make one's reading more fluent. If in the process we produce more Latin speakers, all well and good. There is a demand for learning in this way - no argument about that.