toucanbuzz
No rule is inviolate
I am, though, somewhat uncertain as to how to interpret your report that the DMG speed factor variant did not make player choice matter, but your modification of GI did....
It was the DMG's seemingly minimal 10% modifier (+2 for light weapons on a d20, or -2 for heavy ones) and a comment our Ranger player made. He felt that he was choosing a "quick" (short sword) weapon but it didn't feel like he went first very often. I didn't feel we could move to a d10 system, which lessened the effect of randomness, because of spells (-1 per level) as they'd never go first, and that penalized casters too much.
In a 2nd playtest with new players, we have a rogue who dual wields daggers quite often. Since I'm not getting paid, I haven't recorded our numbers, but it feels like his d4 puts him near the top of initiative orders quite a bit, though not based off his Dexterity.