I haven't purchased a polo shirt
Right there with ya.
I don't put anything in my shirt pockets. Maybe a pen, temporarily, at work - and then only if I'm not suited and booted, which I'm mostly not.
(dress shirts in the UK are different to those in the US. We tend to opt for a spread collar (never ever button-down) and no pockets, whereas US shirts seem to have pointy collars, often button-down, and pockets. We think you look weird and adorably dorky, especially with that super-long-tie thing y'all have going on - with Trump as your SLT king. You of course think we all look and sound like James Bond, which we obviously do.)
Many moons ago, when phones were considerably daintier than they are these days, I had a shirt pocket/toilet phone transfer instantiation incident. I stopped putting my phone in my shirt pocket that day.