That's a common misconception, but thanks for giving your side of the argument. I think that SCR did a great job taking about "Advanced F2L", so I would check out his video right here
Popular YouTuber saying something doesn't make it true.
Anyhow, intuitive versus algorithmic should
obviously be a false dichotomy but for some reason people treat this as a hill to die on and argue forever about how intuitive is better or worse or whatever. (My hill to die on is that this is a dumb hill to die on. Arguments are boring, let's do meta-arguments!)
Oh boy, some people have a really skewed perception of what algorithmic and intuitive F2L are. Let me try and clear it up for everyone. Alg F2L is where you literally learn an algorithm for all the F2L cases and treat it like an OLL or PLL. You see the case, and you execute the algorithm. Where most people tend to get confused is with intuitive F2L. Some people seem to think that intuitive F2L is the same thing as beginner F2L, where you do some inefficient thing that a beginner can understand. This is incorrect. Proper intuitive F2L is where you do the most efficient solution, the "Algorithm" per say, but you understand it INTUITIVELY. You understand why that solution works and what you are actually doing to the cube, instead of just mindlessly doing an algorithm. This is why most people recommend intuitive over algorithmic F2L, as there are no algs to learn and it gives a better understanding of how F2L actually works without harming efficiency.
By
your own definitions (which, let me emphasise, are
not universally accepted, not even by other people in this thread advocating intuitive F2L over algorithmic, which is why people have this argument at all), algorithmic F2L is a part of intuitive F2L. Ergo, it doesn't even make sense to recommend intuitive over algorithmic—you're still learning algorithmic regardless.
You say there are "no algs to learn", when you really mean "there are no black-box algs to learn". Big difference there. You're still learning the algs, just not necessarily in the same way one would learn OLL or PLL algs (reading the algs written explicitly in Singmaster notation).
The difference between algorithmic and intuitive F2L is actually quite striking, Algorithmic F2L means that you just looked at a spreadsheet at called it a day. Intuitive F2L means that you have spent time playing around with the cube to see which moves orient and permute certain pieces, as well as preserving other pieces during an insert.
False dichotomy.
Keeping efficiency in mind, people like Patrick have such good knowledge of the cube, that his F2L pairs are actually, for the most part, more efficient than algs since he is able to take advantage of what the rest of the cube is like
If
you refuse to learn F2L algs that can exploit free slots and such, the inefficiency incurred is on you, not on algorithmic F2L.
This isn't merely a hypothetical; J Perm's F2L sheet includes a handful of algs that can make use of free slots.
The only time that algs are 100% just as or more efficient is during last slot, and even then you can't use fancy techniques like forcing EO so your solve could be even worse off than by just using intuitive inserts.
Consider: 7-move "algorithmic" insert where it's hard to influence EO, versus 11-move "intuitive" insert where you can influence EO by introducing a sledgehammer and thereby increasing it to 12 moves. Which is better? Keep in mind that fruruf takes 6 moves, and do also take into account whether one should be expected to know ZBLL or "merely" OLL+PLL.