AI is changing how software engineers work, but it often comes with hidden burdens and costs. In this paper, we characterize two such often-overlooked burdens: (1) the constant need for human oversight and inspection of AI-generated artifacts; and (2) the growing cognitive overload on software engineers from receiving large amounts of suggestions from AI tools. The need for human oversight is not optional-engineers must review, validate, and sometimes rework what AI produces. At the same time, the flood of AI suggestions, prompts, and possible solutions can leave developers mentally stretched. By blending evidence from recent opinions from practitioners, we highlight these often-overlooked challenges and open a conversation about how teams can handle them in day-to-day AI-assisted software engineering.