There's no good reason regular footwork sequences should be less artistic than this element.
The reasons why leveled step sequences are not primarily artistic are similar to the reasons why spins and jumps (and various pair elements) are not primarily artistic. They are technical elements, whose primary purpose is the demonstration of various kinds of technical mastery.
This is very clearly intentional from the way step sequences have been defined since the beginning of IJS. The technical skills that it is designed to reward include advanced turns in both directions. This is the only element in which those skills are explicitly rewarded.
(They are also rewarded explicitly in the Skating Skills component, and implicitly in the Transitions component, but they are not required anywhere. Except in higher level step sequences. And I think it's pretty clear that the incentive to include these advanced turns and thereby earn the higher levels was written into the rules because so many skaters in the 1990s and early 2000s were giving no evidence during any part of the competition that they actually could execute these fundamental skills at all.)
The only difference in the last couple years with the mandatory bullet points for +4 or +5 GOE are that the "matches the music" bullet point is one of the first three, mandatory ones for step sequences, whereas that bullet point is the last one listed for spins and jumps.
Programs are supposed to be fully cohesive throughout and I don't think the "choreography sequence" should be the one token element between both programs that allows people to have freedom.
It is not.
Skaters have quite a bit of freedom to do whatever they want in spins or step sequences, or even in jump elements, as long as they meet the minimum definitions of the elements.
For leveled elements, there are stricter definitions of how to earn higher levels. But it is not required to earn higher levels -- just rewarded enough that skaters who can do so while also maintaining quality have significant incentive to do so. But incentives are not the same as restrictions.
The current footwork doesn't really have variety though (certainly not as much as we should be seeing).
What kind of variety are you talking about? Variety from one skater to the next, or variety of blade skills by each skater?
The whole point of the variety of steps and turns feature is for skaters to demonstrate that they have mastered a variety of advanced skills. Similar to the Zayak rule, or the limits on repeating spin features introduced a few years into IJS, which encourage skaters to demonstrate a variety of different jumping and spinning skills.
(I personally think there is still more room to reward explicitly even greater variety of jumping and spinning skills, and greater variety of blade-to-ice skills in steps and field moves. That would include more options in step sequences. But I have no problem with reserving Level 4 in step sequences only for those that include the full range of advanced turns. We could brainstorm how rules could be rewritten both to reward those specific skills and to allow for more variation )
Imagine if it was required in footwork to constantly pat the top of your head and rub your stomach as you do it.
Yeah, that takes a specific kind of skill to do, but who cares. We shouldn't have to see it from everyone.
If it were a patting and rubbing competition, then it might make sense to require those two
In a skating competition, it does make sense to offer the highest rewards for the hardest fundamental skating skills.
Novelty skills like toe steps, half jumps, two-foot steps like grapevines, sustained edges emphasizing body positions, knee turns or slides, quick steps on flats, etc., do add variety and creativity, and some of those are quite difficult. And they are rewarded in step sequences, both in some level features and in some GOE criteria. But most of what I have named in this paragraph are not considered fundamental skating skills in the same way that one-foot turns are.
A sequence that consisted entirely of these types of steps, with no turns at all or maybe some threes and mohawks in the preferred direction would not be a good demonstration of advanced skating skills.
I'd classify head patting and stomach rubbing as having more in common with the novelty steps than with the fundamentals of what makes skating skating: gliding and turning on edges.
Professional dance choreographers don't have to throw every type of turn in sequence into every piece they create, why should it be required here? Also imagine if it was required of songwriters to put 6 different octaves in every song they make. That would just be tiresome and overly constricting.
If singers or dancers were competing in a technical sport of dancing or singing skill, the dancers or singers would undoubtedly be required to demonstrate a variety of fundamental technical dancing or singing skills. And if they had to do so within the space of a 3- or 4-minute number, then choreographers or songwriters supporting such competitions would have to provide dances or songs that allow the competitors to demonstrate those skills within the requirements of the number.
Those same choreographers or songwriters would prioritize creativity and communicating with audiences in works created for artistic performances and only include the technical skills that support the particular artistic purposes they're aiming for in each work.
The purposes of technical competitions and artistic performance are not the same.
Similarly, skating choreographers who want to prioritize creativity and communication with audiences over technical skills can do so in skating shows, where they can define the parameters of the programs outside of competitive rules. Or, if you want to compare skating choreography to expectations of artistry in professional dance and song, then something like the Grassroots to Champions Young Artists Showcase would be a more relevant comparison than sports competition.
And choreographers who really want to challenge themselves can choreograph competitive programs with as much artistic content as they and the skaters performing the works can fit within the competitive rules.