I'm torn by this suggestion. On the one hand, even if you can add quickly you probably can't do it instantaneously, and so if you have to add lots of dice often it will slow the game down (unless you use an electronic dice roller, but I'm also sceptical of the randomness of these). Plus, the more dice you roll in a given pool, the less likely it becomes that you will roll really high or really low.
On the other hand, rolling 20d6 for damage is really cool, and those rare occasions where you do get the unlikely rolls tend to be very exciting. On reading the suggestion, something in me just rebelled.
For a high-level one-shot game, and especially if I'm expecting inexperienced players (or don't know), I think that the suggestions in that article match what I would do very closely (and I'm very impressed by the ability to fit 20th level characters on one side of a sheet of paper). For campaign play, I might use something like that... for NPCs. I think, perhaps, players get more of a kick out of rolling lots of dice than DMs, and it's also the case that they have far fewer dice rolls to make.
One other possibility springs to mind: instead of simplifying the rolls by using a two-thirds-constanr/one-third-rolled, there's no reason you couldn't develop a set of look-up tables for the big dice pools. For each pool, work out six possible reasults of varying lethality, and then roll 1d6 to index into the table. (So, if the dice pool was 10d6, the values could be 15, 27, 33, 37, 43, 55. Obviously, the numbers would need to be tweaked to better represent actual probabilities, as opposed to my current generation scheme of pulling them out of thin air.)