Many modern GC systems are tuned for exactly this. It often is called generational garbage collection and the youngest generation is tuned to quickly collect these short-lived and non cyclic objects.
I used to work in this field so I've got at least a decent grasp of what modern GC's do and don't do well:)
Cycles aren't common at all and the answer shouldn't be "let's create a huge complex GC that handles all cases, then down the road we'll optimize for the common case" the answer should be "let's do the sane reasonable thing that handles the common case and push the problem of cycle-management to the programmer"
Also, in general GC's are much faster than reference counting (especially when the reference count updates needs to be thread-safe), so the only reason one would use them is to have deterministic object destructions. These aren't common at all and should not be the deciding factor when choosing a memory management scheme.