What’s the best way to push back against a leader or peer who’s overzealous about adding AI where it isn’t needed?

Push with them and focus on making data AI ready. Adopt a risk model for custom AI projects. Educate folks that you risk getting dummer and being liable. AI responses find trends based on frequency of occurance.  (something mentioned frequently on the internet), which doesn't make it true. Lastly write a policy that requires that a human review any products and assign accountability. Then let them assume the risk. 

I see this all the time. I have even pushed back myself sometimes only to realize later that some of the ideas did prove useful once they were built. When a proposal really feels like for the sake of AI, I lean on hard data. what each LLM call costs, the ongoing complexity it adds and whether those extra layers deliver any real value to the customers. Honestly, much of the pressure comes from the top. Every townhall seems to have the word AI a thousand times, so nobody to blame. So clear numbers and a calm rationale will help cut through the hype.

I recommend a data-driven approach grounded in business value. Start by understanding why they want to introduce AI and listening to what problem they are trying to solve, what outcome are they aiming for, or what pressure (e.g.competitive, board-level) might be driving their enthusiasm? This allows you to reframe the conversation around goals rather than tools.

Then, use tangible evidence like ROI analysis, cost-benefit comparisons, delivery timelines, or even prior case studies to show how a simpler, more efficient approach (possibly non-AI) might better meet the need. In some cases, AI may introduce unnecessary complexity, cost, or risk. By focusing on outcomes and offering alternative solutions that meet the same goals with greater speed or less overhead, you shift the conversation from resisting innovation to optimizing it

My suggestion would be to not look at that as a "push back", but rather as an opportunity to share the rationale. They may have reasons to want to add it, you may have reasons not to. And there are always tangible underlying factors that could be compared from value/risk perspective. Addressing them would only improve the adoption process.