Nothing can be brushed off as implicit unless definitions exist. What are your definitions? Why are you saying there is a delay between the voltage and current?
It is implicit that the current through a resistive load is in phase with the applied voltage. This is based on the definitions of resistance and reactance and their voltage/current relationships This is proved in theory and practice. Nothing can make it otherwise unless the laws of physics are changed, or new ones defined.
If the load has inductance and/or capacitance present then some phase shift will occur but it will be negligible if the load is predominately resistive. This is the case with a filament lamp.
The basic dimmer units are only gates/switches and all that happens is that they are conducting for part of the cyle. As soon as they conduct a resistive load draws current, with no delay. Where does phase shift enter into it?
The effect on the supply is another matter as the current is drawn for only part of the cycle , which may not go down well with the suppliers, but it is not phase shift as v and a are still in phase at your terminals.