The only thing that the skaters are "required" to do in the free skate are some kind of axel jump, a flying spin, a spin in one position, and a combination spin. Anything else, including variations, they can do or not do at their own choice. In fact, they could also leave out any of the above, but if so it's fairly likely that at least one of the moves they did instead would end up not counting.
However, to earn the maximum number of points that they're capable of, the system encourages (which is not the same as requires) them to do the full number of jumping passes allowed including three combinations one of which includes three jumps; four spins (three for juniors); and two step sequences for men or a step sequence and a spiral sequence for ladies. Also it encourages them to include whatever features they can to earn higher levels for their spins, step sequences, and spiral sequences.
Skaters are certainly allowed to do level 1 or level 2 moves if they so choose. Yes, the points earned are lower than for level 3 or level 4, but doing the simpler moves well enough to earn higher GOEs than they'd be capable of with more features would close that gap somewhat and also potentially conserve energy so they could backload their harder jumps and earn more points that way. There are several strategies open to skaters as to how to work the system depending on their individual strengths -- if some strategies have been more common because they make it easier to maximize the points or if some skaters are choosing the same strategies that worked for other skaters rather than those that would work better for themselves, that doesn't mean that the other options are not allowed.
Skaters could even do illegal moves that they would like to do, such as backflips, if they really wanted to, but they would lose points instead of gaining points so it would be kind of silly to do them in competition. Same as in the old system.
There are other moves or variations that used to be considered in evaluating the difficulty and variety of the whole program, such as illusion spins or split flips or inside axels, that do not raise the level of a spin or that earn no points or that earn relatively few points and fill an element spot where a higher-point element could go instead, so in effect the system discourages skaters from including them. These are not illegal moves -- skaters are certainly allowed to include them -- but if the expenditure of energy involved would impact the quality of the rest of the program or if the move would fill a slot that could be better used for an element worth more points, then it's not worth doing them.
We have been seeing skaters doing illusions in their step sequences lately rather than in their spins, since they can help toward fulfilling the full upper body use bullet point there.
The well-balanced program rules and the bullet points for features and levels could be rewritten to encourage more variety. I hope that as the new system evolves that we will see this happen. Meanwhile I also hope that skaters/coaches/choreographers will be more creative in using the existing rules to showcase the skaters' individual strengths, and that judges will reward creativity and quality and not just conformity to the current popular trends. And I hope that fans will watch enough different skaters at all levels and look at the details as well as the general impression to appreciate better the variety and creativity that already exists within the various skaters' approach to the new system.