I was wondering if you would ever change the CI en-route from what was set at the gate? Why would you do this and is it legal or sometimes required?
I'm not sure why "legality" fits onto it (other than as has been said ATC should be told of any major change from flight planned speed) ?
All C.I. is another tool in our tool box, i.e. a slightly clever method of speed control. In our airline we usually use a default of zero for departure/climbout and will change to the cruise CI at top of climb ( the CI the company has flight planned us at is displayed on our fuel plan). However there's nothing stopping us using that old fashioned skill, airmanship, and we often change the CI in the cruise (Long Haul), mainly to control the ETA to try and arrive on schedule, but sometimes we will reduce to 0 to conserve fuel.
Why wouldn't you simply modify the cruise speed manually and see what revised figures for fuel-at-destination, eta, etc.? Wouldn't that be more accurate than a random, en-route CI change?
That's another option available to us (and we're fixed Mach cruise anyway on oceanic sectors) but when flying Economy cruise/descent changing the C.I "carries" the speed change right through the sector (i.e. it modifies the descent all well as the cruise) so ETAs should be reasonably accurate right through to touchdown. We may well a combination of fixed Mach cruise for part of the cruise ( e.g. Oceanic), and then use C.I. controlled speed for overland sections - it all depends on the circumstances.