SH excels as a model at precomputation and then quick retrieval of elements that greatly shorten the computation of contribution and energy (replacing entire parts of an equation by simply looking up based on lights and camera the value resulting from a simpler formula mapped to a spherical space).
Deforming objects are one of those things where, most of the time, a full recompute will become necessary, making them less than ideal. But again, it depends from what, where and how you use SH, which are just a mathematical concept, nothing more.
They also don't explicitly address flickering, but being often used as a precomputation element to be re-used, they often implicitly bring more consistency in temporal sampling, AKA less flicker. So does sample preservation and several other things though.
Again, you seem to confuse a mathematical model with the consequences of some of its implementations.
If you wonder about flicker, as I mentioned in my first post, you are better off studying the basics of sampling and understanding where it comes from first and foremost
It's perfectly possible to have a SH based model inherit flicker from somewhere else, or even produce it, and just as possible to have burte force approaches enforce consistency to the point it won't produce any in the final frames.