"Prostitute" does seem a little harsh--and misses the whole cultural range of mistresses, courtesans, and fine ladies of society. What blindness!
I will admit, though, that a full enumeration of gifts does sound pretty icky. Especially since either he was previously getting value for money, as it were, or he shoulda stopped giving sooner.
(And having once been involved with someone who insisted on flooding me with constant expensive gifts, over my serious protests, I'm not thrilled with how this song would sound if she WASN'T a lady of leisure either.)
But public laments to one's mistress do always make me grin; they remind me of the lovely scene in the Dunnettesque HEAVEN TREE by Edith Pargeter (Ellis Peters), where a group of gloriously reckless university students keeps interrupting a pompous wooer's paid musicians, filling in the second half of each pleading verse with such unhelpful lyrics as "While my hired minstrels dun you/For love at second-hand!"