Regarding cruise power, boeing has limited the max cruise thrust to a lower value. Having some extra power above max cruise allows the a/c to accelerate back to cruise speed even when close to the cruise thrust limits, in case the speed should drop.
While on the subject, our SOP is to leave the N1 Limit on CLB even when reaching cruise, to have that additional power in case needed. Is your company SOP to place it in CRZ when stabilized at cruise setting?
I don't know what the specifics of the limitations are, but in general thrust and temperature limitations are based on a complex analysis of "low-cycle fatigue." While running an engine for 10 minutes above a certain temp (illustration purposes only) will not cause immediate damage, running it at the same temp for 100 or 1000 minutes at that temp may incur permanent turbine blade elongation or other damage or weakening of the system.
The Max Con / Climb thrust settings are envisioned for a on the order of a couple hours at a time (30-45 minutes in a climb, or a few hours after an engine failure), while the Crz limits are envisioned for times on the order of magnitude of 10x those times. Over the life of the engine, the Crz limits are use significantly longer than the Max Con / Climb limits.
My airline has no SOP on which to use in cruise. I prefer Crz, because I don't want to see the larger throttle excursions when using autothrottles. If we run into a temperature inversion or other phenomenon that keeps the airplane from achieving cruise Mach at Max Crz thrust, I will change it temporarily to Climb.