If you were to adjust the rate in which players could buy the scroll with their free TP that would only empower paying players and revert the effectiveness of a solution in the first place though. Because free players would be able to re-roll only once a week in your example (at 19 weeks and simulate a faux “100% chance by 19 rolls” it will have taken a free user 1 year and 4 months worth of free TP for 3 pieces) but paying players could re-roll to their perfect stat nearly immediately at very little cost.
I hate RNG too. Never been a fan. Particularly because I have the absolute worst luck of anyone I know.
If we were even to add RNG stats back into the equation though to your 1 stat limit what we would see is the harder to find stats that aren’t always native to gear (AOE Ratio, AOE Defense, Move Speed) still would only have a 1:19 chance of being rolled since they have no variance and will only ever have a value of 1 once they are rolled. Sure, if you want to get Crit Damage at max +66 it would still be difficult at 1:646… but since everyone would likely want AOE or Move Speed it’s almost a moot point as these are very difficult to find elsewhere in the game. I wouldn’t sacrifice those stats that I can’t find anywhere else just for a little extra damage when I could instead +1 my weapon for more effect in most cases.