I certainly now make the effort to 'drizzle' duriing the image acquisition phase - it doesn't 'cost much' in terms of effort or time, and gives more scope for pre-processing options.
For example, I had been having issues with fixed-pattern readout 'moise' (doe to incorrect Gain and Offset settings on the CCD), but drizzling allowed me to align, stack and eliminate this noise from the Master Light frame.
If you collect lots of Lights, and have drizzle selected during the acquisition phase, then StarAlignment can do that for you. What I haven't (yet) tried is selecting drizzle during the StarAlignment and ImageIntegration proceses. I don't even know what the intended outcome is when using drizzle within PixInsight - the last time I tried any form of 'drizzle' was within Meade's "Envisage" software, working with their DSI cameras, and there then seemed to be two primary choices: use drizzle to get larger images, or use drizzle to get a smaller pixel ratio.
I, too, would be interested to hear from users who have played with the drizzle options.