I would agree that in PVP, you are at a huge disadvantage if the time you have to react to another person's actions is very small. For instance, having to counter a 1sec cast-time ability. I avoid PVP like the plague, though. The same is true for moving out of the "bad stuff" in PVE, such a frozen orbs in D3 on high GRs, where more than one tick equals death.
On PVE DPS I would have to disagree to quite an extent, especially knowing how Blizzard has changed the communication mechanics between server and client a couple of years ago. In the past, the client would block you from being able to spam, for instance, the fireball button in an attempt to send a packet to request the next cast of the spell before the spell has finished casting on the client side. People got around this by creating a macro for each ability with a /stopcasting command, and making use of an Add-on called Quartz which showed your latency as a percentage on your cast bar. When your cast timer enters the section of the cast bar that indicates your latency, you can cancel the current cast, and the cancellation packet would not arrive in-time at the server to cancel it, thus allowing the cast to go through, while you have already started casting a new fireball.
Blizzard removed the client-side blocking of additional ability-use requests, and now you can spam your fireball button to your heart's content, and the server will verify whether the cast is to be allowed or not. Making use of Quartz, you can to a very large extent negate your latency issues, assuming your latency is very stable. From my experience, I have had no issues keeping up with EU-based players when it came to DPS, assuming similar gear. What it came down to more was class balance, gear and my personal ability.
It also seems Blizzard did some bad things in the way they implemented message handling between server and client, and only eventually corrected it after a couple of years (such as the 400ms batch processing of incoming heals).
Unfortunately the latency will always be a problem when trying to be a top tier player, as those precious 150ms will make a huge difference to the end results. But! In 95% of all cases, it shouldn't be as huge a problem as we think, especially just plain PVE DPS.
P.S. I have no idea what "CMs" are
