Cora fan here, so my comments must be viewed accordingly, but AFAIK he doesn't have much say in the budget or roster construction, and even if he knows the team stinks it's not really his job to say so. His only job is get as much as possible out of what he's been handed.
A lot of that might be applied to Breslow at this point, too, if he's been handcuffed by Henry's budget.