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Sure, my thinking was more like "for the price of a good belt you could also get a used watch" (probably the belt would be a bit cheaper, but still I'd rather put the money towards a watch than a belt as I wouldn't need a belt for other stuff - if I do need to really bring stuff with me (water, snacks, maybe even clothes) I'll actually just take my vest. This is more comfortable for me personally than carrying a lot of stuff around my waist, never was a fan of that).
If you really need to bring your phone I'd get one of those belts, and hope it works (doesn't ride up the body etc.) - but actually I'd rather get a cheap used watch (assuming you do already have bluetooth headphones), I have found this to be so much nicer than schlepping an actual phone around.