So I think maybe this is more so a general 'hunch' of mine. It kind of goes off feeling for me so I'll do my best to put it into words.What do you mean?
The short 3-cycle edge comms of the interchange-insert type have to use slice moves, because that's how you can isolate a single edge piece. The only other useful edge comms are the M' U2 M U2 type, which also use slice moves (but keep in mind that you can "split up" one of the slice moves without affecting move count, e.g. M' U2 M U2 = l' U2 M U2 L, both six moves long).
There are short 3-cycle algs that are not commutators, e.g. (R2 U' R2 f2)2 or (R2 u' R2 f2)2. There isn't exactly any rhyme or reason to how they work; they just do.
You can just get scrambles off csTimer or whatever.
The general idea is that, when looking at EPLL/L5EP, the algs feel as if they should be intuitive. In relative similar vein are things such as L5CO, OCLL, WV, which can all be found intuitively ( all 2 gen specifically ). Back to EPLL the main 'formula' is to take out pairs, cycle your U edges, and put everything back together. This is outlined in the 2GB method, however vaguely. This sets up for a completely intuitive 2GLL. In general I'd like to flesh out 2GB since the original proposal is rather unclear and abstract ( I'm a big fan of Imam's methods. HSC was much easier to understand given my background in Guimond and SSC ). anyway, while not specifically coms I feel that they'd still be generally related ( sister ideas I guess ). There maybe not be such a clear formula but thought I'd still ask.