Should an AI tool let you opt it out of its own core job, for specific things?

Working through a design question with SignalAI (AI reads your inbox, texts you when something's urgent) — just shipped a way to tell it to completely skip certain senders. Not filtered, not deprioritized — never read, never classified, never stored by us at all.

The catch: if something urgent ever came from an excluded sender, you'd never get a text about it. I'm deliberately building a hole into my own product's core promise.

My reasoning: for some senders, the right answer isn't "classify this well" — it's "don't touch this at all." A therapist, a lawyer, anything where the ask is privacy, not accuracy.

Curious how others in this space think about this tradeoff — full capability with careful handling, vs. giving users a genuine off-switch even if it makes the product worse at its own job sometimes?