Each of the groups in your list has a fiduciary duty to another person. Transfers of funds from the fiduciary account to the personal account of the agent/custodian/attorney-in-fact/rep payee for anything other than an allowable fee for managing the fiduciary funds (fees aren't permitted in all fiduciary situations) could be a breach of fiduciary duty, and the financial institution facilitating such a transfer could be implicated in any suit by the beneficial owner of the funds to recover funds from the agent/custodian/attorney-in-fact/rep payee.
There is nothing problematic in allowing the accounts to appear together for balance and activity inquiries if the individual who is the agent/custodian/attorney-in-fact/rep payee is the only individual who can view the fiduciary account. But it should only be allowed if there can be a block to any transfers between the fiduciary account and any personal account(s) of the agent/custodian/attorney-in-fact/rep payee.