to_{binary format} does not provide a mechanism for specifying a custom allocator for the returned type.

[davidchisnall]

What is the issue you have?

basic_json provides an allocator that is passed to the types used for deserialisation, but there is no way of specify an allocator to use for the object that is returned by to_bson, to_cbor, and so on. The adaptor for output is explicitly specialised on std::vector without providing a mechanism for specifying the allocator that std::vector uses.

[nlohmann]

You are right, allocators are currently not supported. I think it would be possible to add such support by adjusting the output and input iterators.

[nlohmann]

#2989 is ready to review.