I keep hearing "thickness" thrown around...but I have no idea why...
I assume you are referring to as "throwing around" thickness. The reason I suggest thicker heatsinks is because I see so many people wanting to use cheap/easy to find 1/16th thick aluminum, which is (IMO) quite inadequate. They might get away using 1/16th stuff if they only run the LEDs at 350mA or less, but not all of us do that.
Safer is better than sorry.
Two materials of the same square footage, but of different thicknesses, will have different abilities of heat sinking. But you know that already. LED's will create a hot spot directly behind the star, in the spot you mentioned which is the real weak link (the spot between the LED star and the heatsink). That hot spot is greatly cooled by more mass in the immediate area of the LED. Thickness is a very effective, simple way to do this.
The main concern should be the surface area of the heatsink(to a point).
It is, and nobody is arguing against that, but the use of even thermal two-sided tape seems to be perfectly sufficient. This might be the most important part, but it's actually one of the easiest to accomplish to a sufficient degree.
Here is my point. Would it be better to buy 1" L stock(1" x 1") at 1/8" or 1" flat at 1/4"? I would double my surface area with the L and use the same amount of material(roughly the same cost).
The extra surface area would definitely give you more passive cooling, but is there enough mass right near the LED to wick away the heat? At 1/8" thick, maybe up to around 500mA, I don't know for sure.
I'll test it soon, I have some 1/8" thick flat stock I'll use over a shrimp tank, as soon as my drivers make the ever-so-slow transit in from DX.
Finally, unless you have some reason for "super-cooling" your LED rig I dont know why people get so worried about getting it "cool to the touch". These LEDs will run easily up to 90 degrees C.(you could estimate a thermal drop of about 30 degrees between LED and sink). All 90 degree C does to life is cut it by about 50%. That means that with a worst case temp drop from junction to heatsink of 30C(which is pretty lousy) and getting your heatsink up to 140F...you would have to change your lights out in 6 years when the cost of the original LEDs will probably be close to $1 a piece. So...if you have 24 XP-Gs and you buy a $60 heatsink instead of 2x$5 pieces of stock aluminum all you are doing is spending more money and losing out on the possibility of upgrading in 6 years.
Reasonably good point, especially if using import low-cost LEDs. But buying more expensive heatsinks isn't costing you the opportunity to upgrade in 6 years by using a larger heatsink. You're actually postponing the need to upgrade in 6 years. You may get 10-15 years.
Using a smaller, less effective heatsink is potentially forcing you to upgrade quicker, or forcing you to swap out a blown LED when one fails, which can happen.
We don't know just how much the LED scene will improve over the next few years. It may be leaps and bounds, maybe not. I think spending the extra cash on a larger heatsink is well worth it, but then again, that's the whole point of this thread---- how to save money and still have "definitely sufficient" heatsink. Not "somewhat sufficient".