I'm confused. Is this supposed to be like COLL, except instead of already having edges oriented, you have only corners oriented? But those cases are so few. I mean, are you going to use 'corner control' during F2L?
As I wrote the idea is to use it when you get a CO skip but of course CC is an option if you like to use it as the main LL step.
But there's a bunch of cases in CC, 27 for each position of the pair.
For CFOP, it doesn't make sense to use full CC (i.e. 27 cases for each pair position) since you can insert an edge in 3 moves and do CLS.
BTW; anyone got a link to a page with all CC cases? I'm thinking of looking at a method that is a bit like columns first but here you do 3 pairs, last pair + CC, put 3 FL edges and centres, [wiki]L5EOP[/wiki] to fix edges and finaly PLL. You can speedsolve in 45-50 moves using that =)
I see you wrote a lot of this page:
http://www.speedsolving.com/wiki/index.php/Columns_First_Methods
This line isn't objective and doesn't belong in the wiki, regardless of whether or not it's true: "It is a great mystery why these methods are not popular at all, it is fast, effective and easy but there are very few people that uses columns."
I haven't convinced myself that Cross+F2L is faster than Columns First when both are mastered, but I don't think it's hard to see why Cross+F2L is the more popular speedcubing method. Solving the cross first reduces the number of possible edge, and hence also pair, positions. This makes it easier to make the solution for each case as an automatism (either by directly learning algorithms or as a result of repeating intuitive solves). And automatism (i.e. braindeadness) is great for speedcubing.
Note that the same can be said about Cross+F2L vs. Roux. Are there some Roux or Columns First variations that are better, when perfected, than Cross+F2L variations? Maybe. But in practice we should also consider how much extra effort it takes to master methods allowing more freedom.
I'd be interested to hear what Roux solvers think of Columns First variations. They're a better judge than Cross+F2Lers like me.
By the way, since CF is already in widespread use for Corners First, I don't know how to abbreviate Cross+F2L and Columns First. Note that Cross+F2L includes CFOP, Cross+F2L+MGLS+PLL, etc.