What is the reason for changing the speed reference (IAS or Mach number) with altitude?
Aircraft are limited by both air speed (VMO, affects loads on the structures) and Mach (MMO, formation of shock waves resulting in buffet).

At low altitudes, the speed of sound is high so an aircraft is most limited by indicated airspeed (IAS). At higher altitudes, the speed of sound is lower so the aircraft will be limited by Mach number. Aircraft typically fly towards the upper limit of their speed, so at some point they will have to switch from remaining under the IAS limit to remaining under the Mach limit.

The chart below shows the changes in different speeds as altitude increases, assuming standard atmosphere.


Trend data source, speeds for 737-800

The aircraft climbs at 250 KIAS from sea level. An acceleration from 250 to 300 KIAS is included at 10,000 feet. You can see that as IAS is held constant, TAS (True Airspeed) and Mach both increase.

The switch from 300 KIAS to Mach 0.76 is done at FL280. You can see the Mach speed is approaching its MMO. From this point, both TAS and IAS decrease. After the tropopause, around 35,000 feet, temperature stops decreasing and TAS remains nearly constant.

At FL400 the aircraft levels off and cruises at Mach 0.765, and a step climb to FL410 is included at this speed to show the trends there.

More detailed charts and an explanation of IAS vs. Mach as it relates to climb and aircraft performance can be found here.