The selection of consorts by princes is naturally not just about choosing whoever they want; in the end, the decision still lies with the Emperor. Naturally, if you're favored and ask the Emperor for an imperial decree of marriage, it's not impossible to make it happen.
Moreover, the selection of a consort by a prince is a major consideration; it starts first with benefits. Can the wife's family help provide support? Can they make one's status more stable or secure? It's less about selecting a consort and more about selecting the wife's family, where everything needs to be considered thoroughly.
Chu Hongzheng ranks third among the princes, and his mother is the legitimate daughter of Prime Minister Fan in this dynasty. Apart from the Empress's legitimate son, his status is the most honorable, making the selection of his Prince Consort even more prudent.