Why is best angle/rate of climb indicated in airspeed?
Because determining Vx and Vy has to do with the specific aircraft, specific power output of the engine, thrust from the propeller, etc, which is often a function of pressure altitude and airspeed.

Remember that Vx represents a situation where the aircraft has the MAXIMUM EXCESS THRUST meaning a situation where the difference between the maximum thrust available and and the thrust required to neutralize drag force and maintain straight and level flight is the greatest. 


Images courtesy of BoldMethod

Vy on the other hand is the point where the aircraft has the MAXIMUM EXCESS POWER available to it, translating into the greatest change in altitude for a given period of time by simple conservation of energy considerations.  


Images courtesy of BoldMethod

The airspeed where Vx occurs increases as the pressure altitude increases.  Conversely Vy decreases as pressure altitude increases.  This is due changes in power and thrust outputs with increasing pressure altitudes.  Vx and Vy eventually equal each other at the aircraft’s absolute ceiling, since there is neither any more excess thrust or power available here for climbing.