The 17th century version of Sleeping Beauty by Perrault is the first that involves a ban on spinning wheels, according to Wikipedia. In that time period, didn't many women spend much of their time spinning? How much worse in terms of time and effort is e.g. a drop spindle than a spinning wheel, and how bad would banning spinning wheels be for most people? Would it have been a bit of an inconvenience or a big economic hit?
The 17th century version of Sleeping Beauty by Perrault is the first
The first printed version --- it is important to remember that published versions of oral narratives are only sketches of what was going on (or may have been going on) in the realm of folklore. A motif that appears in print may have had a much longer history before the publication.
That aside, we must “consider the source”: that is, “Sleeping Beauty” (classified in the Aarne-Thompson-Uther index as ATU 410) is a folktale, and as such it was told as fiction, part of the oral “novels” of pre-modern Europe. The stereotypical introductory phrase of “Once upon of time, …” is one of devices that were used to signal to an audience that they were about to explore the fantastic.
“Sleeping Beauty,” like all folktales (as opposed to legends, narratives generally told to be believed), was an exploration of this fantastic world. It was not meant to be taken literally, and the listeners would have understood that the prohibition of all spinning wheels in a kingdom would have been absurd. It would have, in fact, made things difficult for the society.
Spinning wheels were an important component in the production of fabric, being the common means to produce the thread used in weaving (the next step). There were alternatives to turn wool into thread, as you indicate with the drop spindle, but this was an inefficient device compared to the wheel, so the prohibition of spinning wheels would have slowed production and placed a burden on the peasantry.
The prohibition wouldn’t have been the end of the world, but nobility always had to watch its back when it came to angry peasants, so an uprising may have been the result. If this were the real world … but this was occurred in the world of the fantastic, so certain rules of realism are suspended. As well they should be, or we wouldn’t have a great story!