Point of Order:
Paramount is the company that gave us those 50+ years of Star Trek. CBS had nothing to do with it until they lucked into the Trek TV rights in the Viacom break up. The only Trek CBS ever originated is Discovery. If you want to thank them for that and thank them for more of it, feel free. Personally, I'd rather curse them for it.
That said, I'd be worried if we're going to start assuming anyone who is anti-Discovery is pro-Axanar, as I'm on record as stating I have no use for either of them. I think they're both cynical, dishonest cash grabs filled with things that have nothing to do with the Trek I want to see, and if they both got dropped into a fiery chasm to the center of the Earth, I would be sitting on the edge in a lawn chair with popcorn and a Cherry Coke and I'd applaud when the chasm closed up on them.