But given that there is in fact a certain form of "memory" (I actually like how you came up with this term), the chances of hitting the next number close to that first roll seem to be higher. Speaking generally, "not having memory" should be equally applicable to both ends of the rolling spectrum, i.e. to the roll before and the roll after (i.e. hitting 0.02 is as likely, or unlikely, as hitting 99.98 after that first roll). However, if there weren't some "short-range" memory (not speaking about dice here), you would inevitably face a uniform distribution, which is not random (read, you can in fact use these irregularities to your advantage, though not sure about dice)
You state this as a fact but it's backwards. If there was any kind of "memory" in a dice game it could be exploited by the casino or by the player, who could keep betting on numbers "far away" from the previous number to increase their chances. It would be over very quickly, most likely due to the casino going bankrupt. But fortunately it doesn't work like that
It is fascinating that I specifically mentioned that the said may not be applicable to dice ("not speaking about dice here", "not sure about dice"). And here we are with you trying to challenge my point where I made it explicitly clear (and twice at that) it can't be challenged since there is nothing to challenge. Moreover, I explained it further in my post that even if there were some form of "memory" in dice, the house edge would most certainly beat it into the ground making it completely irrelevant and inconsequential in the long run