In a mild climate, the shutters-vs-blinds question is mostly about taste and budget. Here, the sun puts its thumb on the scale twice.
First, durability: the same UV that bleaches your patio furniture works on window treatments all day, every day. Faux-wood slats yellow and warp, fabric fades and goes brittle, and cords dry out - which is why so many Valley homeowners are on their second or third set of blinds at the same windows. A shutter built for the desert, like Sanctuary with its baked-on finish, is covered in writing against exactly that failure by our Everything's Covered Guarantee.
Second, heat: your windows are where summer gets in. A closed shutter insulates at the glass in a way a hanging blind physically cannot, and in a Phoenix August you feel that difference in the room and hear it in how often the AC runs.