The Tur and the Mechaber write in the first Siman of the entire Shulchan Aruch " טוב לומר" (It's good to say Parshas Haman etc.) If they say that it's good then we can rely on them that it's good.
The Mishna Verurah (sk 13) quotes the Bais Yosef the reason to say it so to believe that Parnasa comes with Hashgacha Pratis. The Mishna Verura explains, to believe that
increase in Hishtadlus doesn't help to increase Parnasah.
The Prisha quotes the Yerushalmi in Ms.Brochos (Aruch Hashulchan couldn't find it,) "Whoever says Parshas Ha;man EVERY DAY* will be guaranteed not to miss his Mezonos. (Parnasa)
The Tashbatz adds "ואני ערב" I am a guarantor.
*not only on Tuesday Parshas Beshalach