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You can overload operator new to not use the heap. You can use allocators.

Overloading new (for the purpose, of e.g. adding a thread-local allocator) adds implicit global state that isn't always easy to manage.

Sure, but no more than the standard allocator. Explicit allocator objects are a superior solution most of the time anyway.

Good memory management is never easy on a system level, so if one is overloading new, they'd better be comfortable around the complexities involved.

if you decide to use new/new[], you are bound to use the same allocator everywhere. c++ did not give you a chance to customize your allocation.