We know that "conventional current" is the historical notion of the flow of positive charges. And that, in reality, the charge carriers are negatively charged electrons and that they flow in the opposite direction.
For simple circuits, it makes no difference: a battery in series with a resistor and a lamp has the same behavior whether we think of positive charges moving "left" through the lamp or negative charges moving "right." We can also think about more complex circuits containing nonlinear elements like transistors - again, we qualitatively understand the circuit's behavior in the same way regardless of the conceptual direction.
Are there any circuits whose qualitative practical behavior is difficult or impossible to understand if we're thinking about current flow in the "conventional" direction? Where we really need to think of electrons flowing in the proper direction to understand why a certain LED turns on, or why a frequency response curve has a dip in it at a certain place, or why a certain EMI effect is happening?
Edit: I'm not concerned with intimate understanding of, say, quantum-level processes that happen in semiconductors, unless the notional current direction in such processes has a behavioral impact that would be of concern to an electrical engineer (or a consumer).