Here are my two cents.
I learned my F2L by memorizing all the algorithms, and over time I developed an understanding of how each and every one of the algs works. I currently use empty slots frequently, and I allow my solving order to be very organic (Xcross as well as partial cross solves are frequent for my solving).
I don't buy into this idea that you
must learn intuitive F2L first, and then later on learn algorithms for the more complex cases. If the goal of F2L is to be able to execute a situation mindlessly enough as to allow lookahead, then you need for every case you use to be deeply rooted in muscle memory. So if you learn an intuitive alg that is a "bad" alg (high move count, does not utilize the optimal empty slot shortcut, is not 2-gen when a fast one exists, etc.) then you will deeply root this "bad" alg into your muscle memory. Later on, once you discover what will become your best speedcubing alg, you must unlearn your old case and begin the process of committing the new alg to muscle memory. It is very difficult to change your brain's perception of a case from your old alg to a new alg, trust me on this.
I'll give you an example. When I first learned to
sport stack I learned the cycle routine by watching Emily Fox's then World Record solve video in slow motion. I copied her hand motions exactly (only reflected for left hand) in every way I could. I did this so that I would begin implanting this "good" method for stacking into my muscle memory from the very beginning. I have never done another stack routine other than this one. I feel cubing should be handled the same way, but again that is only my opinion.
Understanding the F2L well enough to solve organically using empty slots, solving pairs before finishing the cross, doing something advanced like occasional Xcross or multi-slotting, using 2 gen cases when they're faster, etc. is extremely important. But as a beginner/intermediate level solver do you think that you will intuitively discover the optimal/best alg for each and every situation right from the start? If you can, that is excellent! But if you are like us regular humans then why risk learning and fully committing some, or possibly many, sub-optimal algorithms into your muscle memory? Then you must spend effort later on to unlearn the bad habits you have developed right from the very beginning. In my opinion the effort spent unlearning the bad habits you developed right from the beginning of your F2L is MUCH more than the effort of initially studying the F2L cases from websites and learning what others do right from the start. How do I know this? I learned many very bad habits with my turning style (wristing, very little 2-gen) from the very beginning and I have spent years unlearning them. I have not even fully unlearned all of my bad habits, but I am making continual progress on this. Why spend months, if not longer, unlearning bad habits when you can just learn it
correctly right from the start?
Again, just my opinion. Don't waste your time with studying only intuitively F2L at the start, and adding the algs to that later on. Just learn the algs right from the start now,
but also study them so you can develop an understanding of how they work.
Chris