Are there any actual pictures of the Zircon? The link shows a Brahmos II mockup.
There is a distinct lack of information, beyond it being hypersonic. Even hypersonic is a squishy enough term to mean a wide range of capabilities.
As to the actual missile theory, the counter argument is that anti-stealth will improve as ship-board radar gets better. Unlike a stealth fighter, a stealth AShM will have to penetrate all the way to the radar source, it has no range to aid the stealth effect. It is important here to note that the US is trying to field two hyoersonic systems.
In terms of advantages, a hypersonic missile has a kinematic advantage over interceptors, if conducting terminal maneuvers it will pose serious challenges to a missile defense. This was a topic of active research, but I don't know if how much was solved, esp as nobody in the west has a hypersonic missile analog.
What is confusing about the Zircon is the range, which is rumored to be ~250nm. That seems to be very short for a modern missile. Maybe the Russians are trading size, 80 on a Kirov, for range?
Last thought, I'm not surprised the Russians beat the US to hypersonics. Russia has more practical experience at hypersonic cruising weapons from the old, massive, Russian missiles.