A founder inbox rarely fails because there is no tool. It fails because the important thread is mixed with newsletters, receipts, platform alerts, bounces, old campaigns, support noise, and half-finished promises.
The first inbox bot should not be reckless. It should find signal, produce a draft, show its evidence, check for duplicate sends, and ask for human approval when the decision is sensitive.
That is the setup I install: a private operator with mailbox context, safe rules, a daily cadence, and a direct chat channel where you can ask, "what needs me today?"