Good comment, thanks for posting it.
In most of these mini-amps the amplifier's internal bulk capacitor is between 3300 uf and 4700 uf and it is generally connected directly to the power input connector. When these caps are drained (which takes about 20 seconds in standby with no AC power) there is a huge rush of current from the external brick into the amplifier to charge those capacitors.
We've likely all seen the mini-amp spark when we connect the power supply to the amp... yeah, there's some current there!
The smps brick itself is designed to get itself up and running then provide it's rated current. However, when those bulk caps are fully discharged and the AC is turned on, the supply has first the problem of getting itself going and then immediately the problem of charging huge capacitors. Many just aren't up to doing that repeatedly on a day in and day out basis. They will provide their rated voltage and current... but that first several milliseconds is a killer that can burn out the input diodes in it's own internal rectifier.
Yes a soft start circuit is a good idea here... Why it's not in these amps is simple enough to figure out... price. It's extra parts and they all add to the cost.
Now to be fair... these little bricks will take that kind of abuse a few times before they die. But it does shorten their lifetime as the main diodes suffer minor damage on each repetition, until they finally give up. Hence my suggestion to just plug the whole thing in and leave it on, but in standby between uses.