The House Office of the Legislative Counsel is non-partisan, impartial, and confidential. Whether transparency has merit or not, tracking provenance would make the office partisan. Is more partisanship in government not a concern?
The second issue with transparency is that communication between legislators and legislative counsel member is subject to the attorney-client relationship. Breaking attorney-client privilege is a serious decision. Knowing how such a change would affect the organization and its members is not something to be taken lightly.
A more convincing argument for transparency would address impartiality and confidentiality. This is pretty clearly a Chesterton's fence type situation where advocating to change a system should anticipate criticisms. Addressing opposition preemptively is an implicit demonstration of knowing why the system exists which is table stakes for changing it.