Why I am still not impressed with pocket cameras.

My wife has owned and used a Nikon P7100 for several years now. It's a nice capable camera and takes very decent photos. However her most single biggest complaint continuous to be the slow boot or start-up time that continuous to be inherent in most if not all pocket cameras, even high end models. She frequently misses shots because by the time her camera is ready, the moment is long gone.
One would think that Nikon, Canon and others would do more to speed up start-up or boot time, by either programming power boost to start-up or adding a sleep mode, where one can turn off the camera, but still being instantly ready for the next start-up. It would also help very much if start-up time would be included in a pocket camera specification.
She would gladly sacrifice some battery life to address this issue.