Actually C malloc, free, C++ new, etc. are really slow functions. Garbage collected languages can typically 'allocate' memory with little more than top of heap pointer increment.
You can implement similar memory pools with C/C++, but it's hard to get right when large allocations are made, compacting is very hard, etc. It does work for limited applications, for example ones that have a lot of short-lived small objects.
Multi-threaded garbage collected languages also don't need locking for freeing objects. With manual memory management you might need to lock the parent object before freeing the child to prevent some other thread from loading a pointer to the free'd child object. Locks are slow, even atomic primitives require slow inter-CPU communication. Garbage collection can avoid that completely. Performance win for gc can be hundreds of percents with 16+ CPUs.