Is heap management that far from the algorithmic headaches of Garbage Collection? Compiled languages typically are "arena allocators" by default and probably do

Is heap management that far from the algorithmic headaches of Garbage Collection? Compiled languages typically are "arena allocators" by default and probably don't hit these similar heap management/paring/centralizing/compaction problems until they do a ton of dynamic datastructure allocations and manipulations. ... and they get to punt to the OS too. I'd certainly believe this isn't a "solved" problem.