Gah. I encountered one of these at GenCon, and halfway through the game, I wanted to throw it across the room.
"So, my first attack is... [clatter] ... oops, 21... [clatter] ... wait, 24... [clatter] ... okay, a 17. That hits? Okay, so 1d8 + 2d6 + 2 damage. That's... [clatter] ... 6, and ... [clatter] ... 4, and ... [clatter] ... 2, plus 2 is 14 damage. Now, my second attack... [clatter] ..."
The d20 never needs a reroll. With your d8 and your 2d6, you can roll all your damage at once!
If you were trapped on a desert island with only one die? Sure, sign me up! But in any other situation, I really can't see the advantage... and if someone insists on using a single dTotal to replace every other die they use, it really slows things down. Annoyingly so.
If he'd had three or four in different colours, it might have been fine. Always roll the black dTotal and the white dTotal for a d20 - if the black die shows a 21-24, take the result of the white. For damage, the black is a d8, and the white and green are d6s.
... but if you're carting around three or four dTotals, why not just have a set of dice?
-Hyp.