Atmega2560 Power consumption

when inactive can be more economical

That is true. However, you waste time / energy going out of a crystal oscillator. Most people use 5 - 10ms as a rough estimate to when a crystal oscillator will stablize.

In addition to that, most chips waste certain cycles (some 1k, some 64k) before asserting the oscillator is OK and starting to run the core off the oscillator.

So putting the mcu into sleep makes a lot of sense if you intend to run it very infrequently (once a second or so).

Some chips get around that with a multi-staged start-up: start-up on rc oscillator and then transfers to a crystal oscillator.

Most people would just pick a chip designed for such (MSP430 for example).

With high frequency tasks here and uncertainty with push buttons (polling), I don't think this is one of those cases where you can benefit from putting the mcu into sleep.