How to tell the current from the amp

The suggestion of getting an amplifier with higher “current” vs just the high output power has been brought up many times. However, this is not an easy measurement one can tell from the product specifications alone. Can someone advise a good way to spot if an amplifier offers “high current”? Also, between tube amp, class a, a/b, and d, if there is a consistent approach to evaluate the current number? And if “current” is so important, why this is not a more easily marketable measure on the box of the product? Another one is the damping factor. Similarly, it’s very frequently brought up when recommending speaker match. Just trying to be more scientific and objective here.