Inaccurate. Crossovers are hardly the only way to show rhythmic knee action (ex:
this series of turns is literally a series of "knee action"), and it's possible to have "speed and motion" and "long lines and elegance" in the same program. The example you tried to use is way offbase too, as Lambiel didn't have particularly long lines, and used more body motion in his skating than Joubert. Long lines and elegance aren't exactly tied to skating skills to begin with; just look at Caroline Zhang for an example.
It would be relatively accurate to say it's not possible to have a program consisting mainly of long edges and, at the same time, have a program consisting of constant steps and turns. However, that doesn't mean it's not possible to see how someone is lacking in quality, just because they are doing constant steps and turns. The depth and security of the edges, the ability to transfer between movements, the ability to move across the ice with proper posture and usage of the blade and knee - all of this can be seen. You can also do deep knee bend while doing many of the transitions that Eteri skaters try to do. Her skaters simply aren't taught to do it or don't have the ability.
People are always doing crossovers in programs anyway. They are not magically extinct just because someone like Eteri is trying to clutter the programs with nonsense. Those times in the programs where the crossovers are happening, the skater's ability with that movement can still be seen. Crossovers have become sadly demonized in this recent era of skating, and it's interesting that you basically try write them off as unimportant. You tried to make it sound like your argument was "both ways to demonstrate skating skills are equally valuable", but in actuality your argument just gives skaters a free pass if you consider them to be doing more transitions. Since, to you, doing more transitions inherently means they should be excluded from other considerations.
Also important, "rhythmic knee action" does not mean "deep knees". One of the reasons why the Eteri school of ice skating is so problematic, is because many of the movements in those programs DON'T have rhythm to them. They are just transitions thrown in for the sake of it. It's easier to do transitions like that with no other purpose, with no specific dance-like timing and meaning behind them, no precise musicality. I had a similar problem with Patrick Chan and how his PCS got overscored - being able to show deep edges and ability to gain efficient power across the ice is NOT rhythm. You can do all the "turns, multi-directional skating, and one-foot skating" you want, but that doesn't mean you are showing complete or satisfying skating. With so many of the Eteri programs, the skater is lacking the depth of edge/knee, AND the rhythm, AND the posture, AND the bigger artistic purpose. This overall kind of skating being so rewarded and normalized is a HUGE problem (for over a decade now, ugh, we've been stuck here basically ever since Evan Lysacek's despicable 2010 victory). The bad judging and the narrowness of the scoring system, and people taking some things written on paper too literally, has perpetuated this hellish alternate-reality state of figure skating that needs to be fixed.