Answer
This is most likely by design rather than a bug — not every field that exists on the underlying database table for an entity is synced to the mobile data layer, and a field that isn't part of that mobile sync set simply won't appear as an option in the mobile Page Designer's field picker, regardless of how many custom fields on the same entity do work there. If a specific standard field you need isn't available, that's worth confirming with IFS Support as an intentional scope limitation rather than assuming it's a configuration mistake on your side.