Ok, idea for a different way of teaching beginners method:
Cross - Normal
Corners - Solve corners on bottom, use sexy move to insert
Middle edges - Line the edge up so it makes a bar with the center, then move it away from where it needs to go. Then do the alg(sexy move), then you can just do these three moves(do F' U' F) to insert it. You can make that part use only sexy and a little intuitive part. Use lefty sexy(L' U' L U) for the left side.
Orient Yellow Edges - Use F (sexy) F' and you're able to cycle through the 3 cases.
Permute Yellow Edges - take the pair out (R U R'), then the alg (sexy), then put the pair back in(R U' R'). You can repeat this until edges are permuted.
Orient Yellow Corners - Flip yellow on bottom, then use the alg(sexy) to orient the corners(normal beginners)
Permute Yellow Corners - With yellow on bottom, take a corner out (R U R'), do D moves so that the correct corner is above the two correct edges, then put the edge back in(R U' R'). Then repeat for all the corners. Then the cube is solved
So with this, you only need sexy move(R U R' U') and lefty sexy(L' U' L U) to solve the cube(with maybe a couple moves added/subtracted, like for yellow cross/corners or something).
(I learned from the Rubik's tutorial and basically did brute force 4lll for LL, so maybe this is the normal method lol)
Here's an example solve that gives comments on how you'd explain it. Be warned, it's over 180 HTM, has more lines then the reconstruction of Feliks' entire Ao5 WR, and has a stupid amount of U U' lol
Okay, I posted this a while ago(~1.25 months) as a way to simplify the beginner's method. After some toying with it(don't worry, I haven't devoted my entire life to this for the past month

), I came up with a way to remove the intuitive part from the E layer edges
Here's what I got:
Middle edges - Line the edge up so it makes a bar with the center, then move it away from where it needs to go. Then do the the sexy move that affects the side where the piece needs to go(i.e: The piece needed to go to the left, so you did a U'(moving it to the right), then did the alg the affected the left side(lefty sexy) (because that's where the piece needs to go). Then rotate the cube towards where the piece needs to go(so if it needed to go to the left, do a y') and do the alg you didn't just use(so if you just did lefty sexy, then do normal sexy this time)
Everything else is the same way as before