As Clive says, the kits are often put together using less than ideal choices of components. In this case, I would guess that the kit uses a switch-mode power supply because these are smaller, lighter, and in particular cheaper than a linear supply, which is the preferred option from a purely technical viewpoint. The linear supply can cope with peak overload without breaking into a sweat where the SMPS can trip internal overload protection. I'm a bit surprised as well that there is a problem, though, but seeing that it appears to be load-related, and is a bit variable suggesting that perhaps it is when all motors are trying to deliver pulses simultaneously which won't happen all the time, maybe it is the PSU. Does seem on the face of it to be the most likely issue. My own machine uses small, cheap SMPS boxes for control circuitry where the load is smaller and well-defined (very cost-effective here) but I use a linear supply for the stepper drivers.