I built a soft start circuit into a power amp I once built that used a large toroidal transformer. People may not know just how high tech (not) such a thing is: when you apply mains power using a soft start circuit, it reaches the toroidal transformer through some power resistors, limiting the inrush current. After a delay, the device shorts out the resistors with a relay. It works, but it is only necessary for high power applications based on larger toroidal transformers that would otherwise keep popping circuit breakers or fuses.
By the look of it, the soft start module used here has its own small linear power supply based on yet another transformer - so by using it, you are placing one of those in the middle of the box. If it's not necessary, why introduce all that extra magnetic flux leakage, etc. into the box?
I have seen series inductive mains filters send an SMPS into self-destructive oscillation (and everything attached to it). So I wouldn't mess about with stuff on the input to an SMPS.
Me, I'd use an external wall-wart and with filtering and linear regulation in the box. Playing about with mains power supplies turns a nice hobby or potential cottage industry into a nightmare of regulations, hum loops and sleepless nights (if you have any imagination regarding what could go wrong).