Depends where you draw the line. An arena allocator per request needs to be managed at least by an app framework, if not the application. It's all layers of abstraction, and one of those layers needs to 0 memory.

The arena allocator implementation for general uses absolutely should not do the zero work. This is specific use case, which can be implemented in an app-specific custom allocator.

That's not what I said. My point was that an arena allocator has to be managed at a relatively high level. Similarly, an allocator responsible for 0 on free would be managed at a similar level. They are orthogonal concepts as you say, but there's no reason 0 on free can't be managed by an allocator.