In my typical process of (perhaps) over thinking it, I'm likely to already have the light in-hand in a low-light setting where I need it for SA. If a threat emerges and I'm justified in drawing a weapon, I'd rather use the light already in my hand instead of dropping it and switching to a WML. This also gives me the opportunity to blind and deter a potential assailant without drawing the weapon.
Of course the huge advantage of a WML is that it remains in perfect alignment with the sights on the target. This is why I feel that a dedicated "fight light" has to be (1) ideally configured ergonomically for one's preferred grip and (2) the user must practice shooting with the light. When I go to the range, my first few magazines are with just the pistol, but all the rest are done using the light. It does take regular practice to do this effectively, but no more so than any other aspect of shooting a pistol.
I regularly do "reps" at home drawing the light and pistol, acquiring a two-hand grip and getting both on target. The alignment is not diffcult at all with a flood beam (like my E2T-MV Tactician), but takes a little more precision with a narrow, high-candela beam. Like all else with shooting a handgun, practice makes perfect.