Princes and Princesses were among the highest authority in the Global Army, but that didn't make them free. Actually, their statuses came with countless limits, duties, and restrictions, often preventing them from pursuing what they truly wanted.
There were exceptions. Khan was a famous one, and the noble families weren't strangers to lost causes or failures who only wanted to dwell in hedonistic pleasures or abuse their authority. Khan had even met one during Rick's marriage, but Rachel wasn't even close to that group.
Princess Rachel Montares was quite the sought-after figure. She was young, beautiful, well-behaved, intelligent, knowledgeable, and perfectly established in the Global Army and noble's upper echelons. She was a promising Princess the Montares family had and was investing a lot into, and she mostly met those expectations.