This assumes cooling system is able to remove the heat from the system in equal rates. And that's really the question everyone was asking IRT this new model. Is the new cooling system able to match or exceed the transfer rate of the old one.
What alternate path are you considering for heat to leave the console? The case itself can get warm, but it's not a particularly effective path.
The cooler-exhaust path is the dominant way to get heat out of the system, and if so then that path in both designs needs to transfer heat at the same rate. Failing to remove 200W of power means heat builds up in the console until something breaks.
What can differ is the temperature of the parts being cooled, since heat flow is proportional to the temperature of the hot side. A good cooler and a bad cooler in isolation are going to remove the same amount of heat at some point, it's a question of how hot the hot part of the system gets until the rates equalize.
One thing that has to be said for people that are dismissing complaints about coil whine is that coil whine is far more subject to variance from person to person because some people are far more sensitive to it than others. While this is also true for fan noise, it's is true to a far lesser degree than coil whine or electrical noise in general.
Coil whine can also be affected by variation between components, the parts they are mounted to, and physical matters like adhesives and the electrical behavior of the load.
Some people report coil whine in specific titles, while others report hearing little coil whine in those games, but in others. It's also not apparently a phenomenon of just the most demanding titles. As an acoustical phenomenon, it could mean it's not just the people's sensitivity or hearing that varies, but resonance points in the hardware coupled with whether the games they run hit those points.
A console whose parts happen to have variances that don't line up in a way that resonates in an audible frequency or one that is more readily baffled by the case would be mostly silent. A fraction of the millions of units getting an unlucky combination seems plausible, particularly since Sony has a history of more variable construction--since not everyone complained about a jet-engine PS4 Pro. There's also at least three fan models in play across the production pool as well.
The Series X PSU's heavier use of coatings would help interfere with resonance in audible range, and help absorb vibrations in general.