It would be a great thing for IMAP servers to do, but none of the major open source ones really take on that feature, and Google wants you in their web-client, so searches via IMAP are low-quality at best.
Doesn't this feel like a perfect example of work done at 3AM when plugged in and (importantly) after the battery is fully charged? It won't be perfect, searching for an email in the afternoon that you received in the morning won't be in the index, but I generally don't need search for emails I received so recently anyways