I asked developers about this as I feel the same way @chan feels.
Primary and secondary organizations are supposed to behave the exact same way.
This means custom objects shall not be readonly only just because you’re with a secondary organization.
Above statement expects this happening on vanilla installations without core workflows or similar adjusting the availability of a field.
If that’s the case for you, please create a bug report at Issues · zammad/zammad · GitHub and mention this thread so the verification process is faster. Thank you!