Matthew's been asked this before and I've never seen him respond to the question, not that he hasn't addressed it. He undoubtedly knows that poche is a fraud, but I suspect the two reasons he allows him to stay are because poche unwittingly gives trad Caths an opportunity to sharpen their teeth against typical modernist errors and because poche's behavior generates activity.
The "Poche is a challenge to us" theory is one I've never bought. The other proselytizing heretics I mentioned fit that bill infinitely better: Icterus because he was actually intelligent and more or less intellectually honest when engaged in debate, and Trickster Bruce because he at least gave lip service to the notion that he was willing to learn about Catholic Tradition. Poche, on the other hand, has never shown that willingness, and, worse, refuses to answer directly or clearly when faced with a question that endangers the narratives he propagates (case in point, despite his regular spanning of the forum with the "whoever exalts race" passage from Mit Brennender Sorge, he refuses to ever respond directly and honestly when someone asks if he agrees with the encyclical's acknowledgment that race is a "fundamental value of the human community" with a "necessary and honorable... function in worldly things," or if he recognizes that the Jews are especially guilty of "exalting race above its standard value").
Icterus and Trickster, furthermore, didn't artificially hike up their post counts with copy-paste human interest fluff from Yahoo News or interminable updates on whatever "butter and cheese-soaked" atrocity they'd been subjecting their colons to. In that alone, they demonstrated more good will on this forum than Poche ever has. They too "generated activity" and yet, they were banned within a month. And Poche? Well, this gives one a sense of how long he's been a problem around here: https://www.cathinfo.com/general-discussion/ban-poche/
Poche suddenly appeared on Cathinfo (and Fisheaters, CAF, etc.) in the summer of 2012 and has been shilling on behalf of modernism unabated ever since (though FE, to their credit, eventually banned him). He has racked up a post count on the various forums that numbers into the tens of thousands.
For the record, I am 100% convinced he's a Novus Ordo "priest" or "deacon" whose "vocation" is conversion of us wayward Trads to the waiting arms of the Church of the New Springtime. His very moniker "poche" - an architectural term that refers to the black spaces in a building plan that denote solid areas of the structure which are concealed behind walls - implies hiddenness and subterfuge (though its allusion to Poche's thickheadedness is particularly apt).
Anyway, it looks like he's here to stay, so break out your guitars and tambourines: