Good for you that you don't believe it. You are wrong. I say it does. Prove me wrong or just attack me again, your choice. Or chose to engage where you have something useful to discuss.
I already "proved you wrong" as you put it, re: initiative being "faster for some groups" without any qualifications as to the conditions under which that would be true.
Sure, it speeds up play at our table because it keeps all players engaged constantly. Yes this is a thing because guess what? Not everyone plays the same way you do. We play virtually. And yes, when you play virtually it becomes a real thing to maintain player's attention for minutes on end when they have no reason to pay 100% attention. With re-rolling init, they have a reason to pay 100% attention. Therefore when their turn comes around they know what is going on. They have been thinking about it. They have been playing out the scenario real-time in their head.
Yes, there are other ways to address attention issues. This one works for us and give us lots of other benefits we enjoy.
Why are you so hell bent on proving me wrong?
See, now we're extracting some useful information from you, rather than illogical claims seemingly based on anecdote. So to answer your question - I'm not "hell bent on proving you wrong" - I'm trying extract some useful information from you about why you think what you think.
So what we're seeing is a considerably narrower and more specific claim that what you previously made, and one that's more plausible. Specifically that:
A) If your players have really significant attention issues, like those some people have when playing online, then forcing people to make this roll and re-order initiative causes people to have to pay a bit more attention, and presumably then not just "wait for their go".
B) This isn't the only solution to that, nor by implication, necessarily the best one, merely one that works for you.
That's fine - that makes sense and is actually a useful bit of information.
Without random init, I have 2 players in my group that will solve the battle mathematically on turn one, if they chose too. They are that good at math and RPG tactics.
But denying the possibility of such a table existing among millions of tables playing D&D is arrogance that no one could do something you can't.
It's not really arrogant to disbelieve extremely wild claims - I'm not arrogant for thinking that my second cousin probably didn't
actually see a werewolf that one time, sorry. Nor is it "disparagement" to disbelieve this. I'm not saying you're liar - I didn't suggest that, because I don't think it's the case - I think you've got an inflated and laughable opinion re: the capabilities of your players. Which is cute but silly rather than a malicious deception. And it's not a "millions of tables" statistical anomaly thing. "Millions of tables" things are like rolling straight 18s down the line on 3d6 chargen, or rolling 10 natural 20s in a row. Hell I've seen somewhat similar things. But D&D combat is flatly not possible to "solve mathematically on turn one" as you claim, because there is simply too much variance and because of information asymmetry.
Further, even if it was possible to "solve it mathematically on turn one", simply adding a few more instances of one specific variable (initiative position) to the dozens to hundreds of other variables wouldn't likely make it impossible to solve.