Not sure how this is related. A general purpose allocator with a plain malloc interface can’t use this to do anything useful wrt lifetime because there is no correlation to lifetime provided by the interface. Internal arenas can be useful to address contention and fragmentation.
I'm pointing out that an arena is more about "a region of memory that you can split up to use later" than "a region of memory that must be allocated and deallocated all at once".
I've never heard that use of the term "arena". Are you thinking of slabs? Arenas are typically allocated and deallocated at once. That's their main feature.