GMail search fundamentally has an advantage over a mobile email client as Google can and does maintain dedicated indexes for your email on their servers. While a mobile client could do the same, it's not really something that you want to do on a battery-powered device.
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.
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.