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