What is the very common culprit component(s) and what is its
function within SMPS having weak current, far weaker than its rating while its voltage and so likely most of others are always perfect?
Another guess, and it is only a guess: Current limiting is triggering early.
Depending whether this function is implemented on the primary or the secondary, how the current is sensed (shunt, transformer, hall), the controller’s CS implementation, peak or average limited, and other details, it could be a couple dozen different things.