Just out of curiosity as well as from having designed CoFs that have required the use of a tactical light: ...I'll go first with my answers in (), be they in the minority or majority of others' responses...
1. Of folks who carry a tactical light daily (yes, I do), how many actually have a lanyard on it (no, I don't)?... and where do you normally carry it when NOT in a situation where you feel you need to have it ready in hand (for me, either shirt pocket, pants pocket meant for the light, or jacket pocket meant for the light)?
2. Of folks who carry a tactical light daily (yes, I do) and your situational awareness suddenly has you take out your tactical light to be in a ready position for either use as a light or even as a skull punch-out tool, do you have it in your support hand ready to do either of the above with or without a lanyard (me, without since I don't use a lanyard) or do you take the time (which I would find time-consuming to do) to put the lanyard on either my support hand or around my neck in a "sudden" situation?
3. Of folks who carry a tactical light daily (yes, I do), how many of you "practice" removing it and holding/using it during dry fire and/or range fire (woops, I don't as much as I should)?
I can't speak for why IDPA has the rule as it does regarding lanyards as well as starting a stage with it in your support hand, but I can take a stab at it: 1) in our CoFs in which I have designed them for the use of a tactical light (which we have done in the past last year, but, hint hint, we will be doing in the near future in this current season), the scenario of the CoF already has you in a sudden situational awareness, i.e., not one that you can see from a mile away (hyperbole here), which basically forces the shooter at the P1 position to be at the ready with a tactical light in the support hand (since that is the IDPA sport's rule) and a hair (timer buzz) away from taking action with your handgun in a critical incident. 2) perhaps a lanyard can serve as a possible means for the perp in a close-up FoF encounter to get into a tug-of-war with your lanyard to gain control of it.
Thanks for taking the time to read this, try to make sense of what I wrote, and to answer if you so choose to do.