Chasse is good for short distance. Crossover is good for long distance. Crossover is the fastest and easiest way to gain speed. Hanyu does not use many crossovers to gain speed, for the like of him, using such easy tool to gain speed isn't ideal. So for Hanyu to use chasse to gain speed, it's quite interesting as this move is for short distance but he still gains much speed thanks to it. This is why his skating is amazing.
I can see in Hanyu the preference for intricate footwork which looks more effortless and rhythmic than most men out there. Chasse is originated from ballet, it is rhythmic but harder to use for long distance. However it helps creating a flowy feeling of the skating, especially with his flexible knee bend that move with the music.
In short, Hanyu uses a short distance move to gain greater speed than most other skaters who use the move for long distance. This method is not new, some old coaches are still thinking the same style. For example I think Brian Orser's old coach, Doug Leigh also has the same mentality. He once gave Brian Orser a program without any crossover at all.
In the latter generation, my Russian coach doesn't like it when a skater does more than 3 crossovers in a row. Hanyu is the only man I can think of to qualify her criteria (maybe Chan at his prime also).
Among ladies, I would say Tutberidze's students fulfill that idea very well. Medvedeva and Zagitova and that very tall girl I forgot how to spell her name. They all use very few crossovers. Only 6-8 crossovers in the short program. Some people might complain that these Tutberidze's girls are slower than other girls but using less crossovers is very good for them in the long term. As they develop their skating, using more difficult turns on 1 foot continuously will help them to improve their skating skills. I think Tutberidze understands basic skating very well and she is applying the robotic way, less organic style on her students but it's very down to earth and help her students get fast results. She originated from ice dance after all. She doesn't let her students abuse the crossovers aka the more labored way to gain speed.