C++11 introduced a GC API in the standard library, and one of the biggest C++ game engine does use GC in their engine objects, Unreal.
C++ on Windows makes heavy use of reference counting (which is a GC algorithm from CS point of view), via COM/UWP.
The biggest problem to overcome is religious, not technical.
Not sure if Ref counting is a good example here, as there is no runtime monitoring the object graph hierarchy and of course Rust it’s self uses ref counting in many situations.
Reference Counting is a garbage collection implementation algorithm from CS point of view.
RC has plenty of runtime costs as well, cache invalidation, lock contention on reference counters, stop the world in complex data structures, possible stack overflows if destructors are incorrectly written, memory fragmentation.