Which struck me as an odd way of looking at it, but, whatever,
I think it was a really useful contribution in that it highlighted the aspects of the luck mechanic that actually matter: that is to say, the probabilities of success. The normalish curve you get by plotting probabilities of each individual roll doesn't really tell you much in itself, since you're never aiming for an exact roll, just to exceed a threshold.
And I thought it was helpful to note that you can't just switch to 3d6 and leave your DCs alone, because you're completely changing what DC 15 means, for example. It's like going from the U.S. to Australia and getting $15. You can have $15 in either place, but the number 15 only means something in a particular context.
For example, if we want to define a "fairly difficult" task for an average PC without training (figure a +1 ability mod as average) as something for which they have about a one in three chance (35%) of doing successfully, then when using 1d20 rolls, that makes the DC 15. If we want to define a 1/3 success task for the same character in a 3d6 system, then we need to set the DC around 13.
And then we can ask "what do we think being trained should do on a task that an untrained person can do with 35% success?" and ask the same question for other levels of difficulty, and for being an expert vs being trained.
The answer that RAW gives to all of those questions is, "it should increase the chance of success about 10%, increasing to 15%, then 20%, and eventually up to 30%". And this answer is the same regardless of the starting difficulty, obviously with the caveat that the chances can't go below 0 or above 100%.
The answer that you are implicitly giving if you switch to a 3d6 resolution mechanic and don't adjust bonuses or DCs is that the average untrained PC should succeed 1/3 as often at so-called "moderately difficult" tasks, and fail 1/3 as often on their "fairly easy" (DC 8 with a +1) counterparts, that on "fairly difficult" tasks, proficiency should raise your success rate by about 21% initially, and eventually about 67%, whereas expertise should initially further raise it an additional 25%, and eventually an additional 58%. On the other hand, for "fairly easy" tasks, proficiency should initially raise your success rate about 12%, and allow you to auto-succeed by level 17, whereas expertise should allow you to auto-succeed from level 1.
I think there are some nice aspects to that, but it's useful to realize that it's not
all that different from making the proficiency bonus start at +4 and scale to +12 and adjusting everything else accordingly (most of the differences amount to less than a +/-1 on a d20 in either direction depending on the DC and starting bonus).