Will a running belt fit a large phone like an iPhone Pro Max?

Some will, many won't. The Sporteer Kinetic K1 is explicitly built for phones up to a 6.8" screen and is the pick most often recommended in r/XXRunning and r/Marathon_Training threads about Pro Max-sized phones. FlipBelt's tube design also accommodates large phones, while smaller zipper pouches like the original SPIbelt can be a tighter squeeze depending on case thickness.