I think it might be more useful to consider the basic lateral movements as tools that you use to improve the horse, rather than elements that you school. So in that frame of reference, yes, you continue to utilize those tools to address issues. For example, my mare can tend to forget that she has hind legs, so we use TOF to get her moving off my leg and engaging for a crisp W/T transition. My instructor had me use this for W/C transitions on a more advanced horse. It’s not about perfecting the form of the TOF, it’s about using the tool to achieve better work from the horse.
Similarly, quite green horses should be starting to get familiar with LY, if they are being ridden on circles, to develop bend around the inside leg, and learning to carry weight on the outside pair of legs, rather than “motorcycling” around turns. If the horse can yield a little from the rider’s inside leg on a circle, it’s not much of a stretch to start a more traditional leg yield on a straight line.
It also depends on the particular horse. Even though my horse is more TL/working towards first, I use SI, CSI, travers, renvers and sometimes a bit of HP at the walk to help her come together, because she likes to go long as a bus (daddy was a western pleasure type quarter horse) and tends to be stiff in her spine. I’m not sure how much I’ll use TOF with my 4 year old when I start her, because she is one who tends to ground her front feet and disengage her hind legs naturally, so I might focus more on making sure I can move her shoulders as easily as her haunches. I think TOF could turn into a weapon she would use against me until I have her pretty confirmed at inside leg to outside rein. This is to say, there is not a cookbook order of introducing and employing the lateral movements.