Three hundred sets, and just in Capital City, there are nearly thirty aristocratic families of all sizes. Since they are aristocratic families, when you add up all the legitimate and collateral relatives, there are at least a hundred people—this lady, that lord, this young master, that young miss. Even just one set for each household certainly won't be enough.
Apart from the aristocratic families, Capital City also has those high officials—most of Daqi's highest officials gather here, adding up to several dozen. These officials have many in their households too, including lords, ladies, young masters, and young misses.
Then there are the wealthy folks. Half of Daqi's rich are in Capital City, and these people also want to keep up with the latest trends. Moreover, such entertaining and novel items are perfect for giving as gifts, whether to curry favor with nobles or to impress friends and relatives.
How could one set be enough? At the very least, you'd need ten sets or more!