based on a lot of royalty series i have watched, princess training is basically etiquette for the palace, how you sit, how you greet and stuff.
it is almost the same as etiquette at work. (pleasr dont tell me youve never heard of etiquette at work your school taught you that)
you need to learn that as a princess, a crown princess at that will serve the soon to be king so you must know how to serve him and satisfy him. thats why people who enter the palace will need to learn on how to survive in the palace
is it mandatory? yes. if you dont know the etiquette and you dont know how to survive in the palace as a princess/prince/royal you could get killed any moment since not everyone can be trusted in the palace.
imagine if one day someone sent you a letter, and its all in old chinese letter, and you cant even read. what if the letter was about to warn you about killers in the palace, you dont know how to read and boom. KO.
hope that helps.
Bro what's with the princess training thing? I just saw those words and my brain already left my head