Thus the tachometer is the best indicator of best climb-angle (and best climb-rate) in a sustained climb.
Correct but not the entire picture....In a fixed pitch propeller aircraft, the tachometer is your primary engine instrument for establishing climb power.
Airspeed is your primary for establishing the L/D ratio you want to be at to achieve best climb rate. It represents the ratio of dynamic pressure to lifting/drag pressure that is fixed by the physical shape of the aircraft to achieve the L/D ratio where combined with the engine power settings is the point that Power Available to Power required is maximized.
Because those ratios occur at a specific angle of attack in a fixed relationship.....
In a World War I aircraft without an airspeed indicator, this would be the Angle of Attack based on the angle the little string tied to the strut shows us!