To be fair, I do that. 2-3 times a day, in fact. Not all of my emails (the archive has ballooned to several hundred thousand messages total), but the most recent ones certainly.

My standard prompt is along the lines of "go through the last N days of my emails, identify all threads that I need to know about, action on or follow up with". N is usually a number between 2 and 5. I've specified a standing of set of rules to easily know what is likely a source of noise to aid in skipping the bot spam.

The company is charged API pricing through an enterprise contract, and I remain persistently curious how much I burn. My daily admin-related token expenses appear to fluctuate between $1 and $5. For something that saves me up to 2h of time a day I consider that a rather tolerable deal. (When I dive in to code to do refactors or deep investigations, I can spend as much as $25 a day.)