I disagree, I think the tradeoff is done differently. CFOP has different periods of restriction, many of which are superior to Roux. As fast as Alex is at <MU>, TPS simply doesn't compare to CFOP's move restrictions <RUF> for example. CFOP is less efficient (assuming a high level Roux solver), but also less complex/adlib. CFOP solves are so similar that there is practically no thinking time. This allows much higher TPS than Roux.
In most cases I would rather do 8 moves of <M,U> in 1 second than 11 moves of <R, U, F> in 1 second, which I think is the context we should talk about this comparison in. Firstly less moves generally means less opportunities for major or minor mistakes in turn accuracy, secondly <M, U> stance is generally 0 regrips whereas plenty of <R, U, F> algorithms tend to have 1 or more full or semi-regrips. Imo economy of movement is a plus for several reasons and that's harder to achieve with turns around a vertex like <R, U, F>.
Other restrictions I forgot to mention are things like CFOPs reliance on maintaining D layer edge positions - I think some 2x2 CLLs are good examples of how alg design changes, though that's not a direct comparison. One can ignore or bypass ending every f2l alg with correcting a D layer edge but it really ups the complexity and you generally don't want to do it to maintain speed.
The way I tend to envisage it is that everything you do in CFOP prior to the LL is always done with the intention of preserving the unsolved-ness of the U layer in combination with the solved-ness of the D layer edges... This creates certain types of restrictions as a trade for simpler lookahead, in turn creating simpler solutions. In contrast, until CmLL, Roux solutions are done in respect to preserving the FB (which is kept in your non-dominant hand anyway) and whatever you've currently built of the SB.
Edit: Oh yeah, basically didn't respond to your point, sorry. Although I respect your point about it being done differently (TPS rather than efficiency, simplicity > complexity), I think the ceiling argument still applies - the room for improvement in f2l basically comes from pair selection which in human application will probably never shave off more than one pairs worth of moves (and this is with a lot of experience and lookahead) from the average f2l. I remember a long time ago Breandan spent a good while working a very restricted approach with lots of esoteric f2l algorithms but abandoned it in favour of just 'better standard solutions'. Basically I'm trying to say that CFOPs approach reaches a physical tps/reaction time limit at around consistently 9-10tps and to increase efficiency from that point is very difficult simply due to method design...
That being said I wouldn't be surprised if Feliks can now sub-2 every possible LL, I don't keep up with stuff that much right now.
Expand on this please, I think you are overstating CN's advantage. You don't need colour neutrality to inspect cross+1. Also inspection time is far more influential on Roux than CFOP.
The parts I didn't quote I don't necessarily have anything to say about, but you make some assumptions/broad statementd that you imply are fact. I'm not sure this method advantage is nearly as clear as you think
I actually don't think I've stated CN's advantages enough, my point isn't about how CN helps you see further, but how CN gives you options, and options are power. Without actually doing any computation or hard research for numbers, being CN basically gives 6 opportunities for a random cross rather than 1, massively lowering variance not only in number of times you receive terrible cases, but in several other respects when we actually count what we're looking for in inspection. First pair is also incredibly important too, along with ergonomics, and distance of lookahead (the difference between seeing the corner of the second pair and not seeing it is pretty huge). Overall 'start quality' is much higher with CN when you can make a choice between several 5-6 move crosses with different options for FP. For loose analogies (but ones I believe you know) it's sort of like getting last pick every time in League of Legends, if you had no preference for role or champion, or if you got one of the late positions every time on a poker table.
Oops, just re-read what I said about inspection time, I think it's pretty clear Roux requires it more than CFOP! More I just meant CFOP with proper use of inspection is very very different to CFOP without, and I wanted to give the idea that this variance is why CN makes such a difference.
You are probably right about how the advantages are less clear-cut than I claim, but I really wanted to write a mini-essay (polemic?) highlighting a few factors I'm not sure have been discussed. Regardless I'll happily defend/debate the overall idea that Roux lies at a better position on the speed-efficiency trade-off curve than CFOP does.
