the Deputy Attorney General may exercise all the duties of that office
I see 2 (two) possible interpretations of that clause. Please be aware I do not know the context of legalese etc.
1. The DAG MAY exercise, meaning he is a possible choice to assume the duties of the AG.
2. The DAG MAY exercise, meaning he has a choice to conduct all the business of the AG during a vacancy.
While I MAY see two possibilities, the reader should try reading putting different emphasis on the word MAY, and see if it is just me or is there some ambiguity of language.
I've dealt with this issue before (succession questions), so the wording here has both legislative and legal significance which is different than posited.
The "may" is permission
from the legistature to conduct the business on behalf of the agency/United States, not to give the Deputy, or anyone else,
discretion to do so or not. This is to prevent the
agency from being unable to conduct business because the head of the agency is absent. In some agencies, duties of the "principal" may
not be delegated (there are several for the A.G. that are exclusive to him/her). This changes that so that, for example, the Deputy A.G. is allowed to supervise the Special Counsel
because the A.G. is unable to, since that supervision is exclusive to the A.G.
The problem with Whitaker, which Maryland has raised, is that if he is not a legal choice for the position he
cannot conduct business as head of the agency (e.g.
may not). In that case
only the Deputy A.G. can conduct that business.
Although there is a corner-case basis for appointing Whitaker, there are
at least three that
preclude him from doing so. I say that, although the DOJ under Gonzales issued an opinion that argued otherwise (using, as was the Bush way, bad legal analysis). That issue was not, to my knowledge, litigated as his appointed "successor" only served for two months. It is the nature of the GOP to use legal legerdemain to pervert or avoid actually applying the law as written.