Not anymore.
You're absolutely right that one of the reasons moving collectors were not used more widely was that, while their throughput was always very impressive, their latency wasn't that great, but that changed a few years ago.
E.g. Generational ZGC in OpenJDK (released in September '23) introduces hiccups or "pauses" that are not dependent on the size of the liveset and are no larger than latency hiccups introduced by the OS (assuming no realtime kernel), i.e. <1ms (and typically <<1ms) up to heaps of 16TB. In fact, the latency can be smoother than approaches that have an explicit free operation and require maintaining a free list, as freeing a large object graph can be quite slow and occur in surprising places.
So modern moving GCs no longer have a latency penalty, but this is newer than even ChatGPT.